Free NEET Physics multiple-choice questions on Equations of Motion 1D. Attempt each question and reveal the answer with a full explanation.
An object is thrown vertically upward with a speed of 30 m/s . The distance travelled by the object in the last second of its upward journey is: ( g = 10 m/s 2 ) 5 m 10 m 15 m 2.5 m The position x of a particle moving along the x -axis at time t is given by x = 2 + t - 3t 2 . At what time t is the velocity zero? 1/6 s 1/3 s 1/2 s 2 s A particle starts from rest and moves with a constant acceleration for some time and then decelerates at a constant rate to come to rest. If the total time of motion is T , the maximum velocity attained by the particle is: T + ( + )T 2 2 T + T 2 + A point moves with uniform acceleration and its velocities at three points A, B, C are u, v, w respectively. If AB:BC = 1:2 , then v 2 is equal to: 2u 2 + w 2 3 u 2 + 2w 2 3 u 2 + w 2 2 u 2 + w 2 3 A stone is dropped from a rising balloon. The balloon has been ascending with a constant velocity of 10 m/s and it is at a height of 45 m when the stone is dropped. How much time does the stone take to reach the ground? ( g = 10 m/s 2 ) 3 s 4.5 s 9 s 1 s A bullet loses 1/20 of its velocity after penetrating a plank. How many such planks are required to stop the bullet? 11 20 10 19 A bullet is fired into a wooden block. It loses half of its velocity after penetrating 3 cm . How much further will it penetrate before coming to rest, assuming constant retardation? 1 cm 2 cm 3 cm 1.5 cm A body is falling freely from a height h . The ratio of the time taken to fall the first half and the second half of the distance is: 1 : ( 2 - 1) 2 : 1 1 : 1 ( 2 + 1) : 1 A ball is thrown vertically upwards from the ground with a speed of u . If it experiences a constant air resistance which produces a retardation a , the ratio of time of ascent to the time of descent is: g-a g+a g+a g-a g-a g+a 1 A point moves with uniform acceleration and v 1, v 2, v 3 denote the average velocities in three successive intervals of time t 1, t 2, t 3 . Then (v 1 - v 2) : (v 2 - v 3) is: (t 1 + t 2) : (t 2 + t 3) t 1 : t 3 (t 1 - t 2) : (t 2 - t 3) 1 : 1 A stone is dropped from a height h . The time taken for the stone to travel the last metre of its fall is 0.1 s . The height h is approximately ( g = 10 m/s 2 ): 5.5 m 10.2 m 2.5 m 15.8 m A bullet is fired into a wooden plank. It loses 20 % of its velocity after penetrating 3 cm . The additional distance it will penetrate before coming to rest is: 3.67 cm 2.5 cm 5.33 cm 1.2 cm An object moves from rest with a constant acceleration of 5 m/s 2 . The distance travelled by the object in the 5 th second is: 22.5 m 25.0 m 20.0 m 12.5 m The acceleration of a particle moving in a straight line is a = -kv 2 . If the initial velocity is u , the velocity v after time t is given by: v = u 1 + kut v = u e -kt v = u - kt v = u 1 - kut A car accelerates from rest at a constant rate for some time, after which it decelerates at a constant rate and comes to rest. If total time elapsed is t , the maximum velocity is: t + t - ( + )t 2 t + A bullet fired into a wooden plank loses 1/3 of its velocity after penetrating 4 cm. The further distance it will penetrate before coming to rest is: 3.2 cm 2 cm 5 cm 1 cm A particle moves along a straight line with retardation a proportional to the square of its velocity v . If the initial velocity is u , the velocity at time t is: u 1+kut u e -kt u - kt u 1-kt Consider a particle moving along a straight line, whose position as a function of time is given by s(t)= t 2- t+ , where =1 ms -2 , =6 ms -1 and =5 m . The average speed of the particle, in ms -1 from t=0 to t=6 s is: 12 6 3 0 If a particle moves with a velocity v = 4 i + 3t j , what is the acceleration of the particle? 3 j 4 i 0 4 2 + (3t) 2 A stone is dropped from a height h . The time taken for it to reach the ground is T . The time taken for it to cover the first h/4 distance is: T/2 T/4 T/ 2 3T/4 The position of a particle along x-axis is given by x = 2 + t - 3t 2 . The ratio of its initial velocity to its initial acceleration is: -1/6 1/6 -1/3 1/3 A body is dropped from a high tower and at the same time another body is projected horizontally from the same tower. They will reach the ground: simultaneously dropped body first projected body first depends on mass A particle moves along a straight line. The ratio of the distances travelled by the particle in the 1 st , 2 nd , 3 rd and 4 th seconds of its motion, starting from rest and moving with uniform acceleration, is: 1 : 3 : 5 : 7 1 : 2 : 3 : 4 1 : 4 : 9 : 16 1 : 1 : 1 : 1 The position of a particle is given by r = 3t i + 2t 2 j + 5 k . The acceleration of the particle at t = 1 s is: 4 j 3 i + 4 j Zero 4 j + 5 k A bullet fired from a gun with velocity v can pierce a wooden block of thickness d . If the velocity of the bullet is doubled, the thickness of the block it can pierce is: 4d 2d 8d d/2 A body is thrown vertically upwards from the ground. It reaches a maximum height of 20 m in 2 s . After what time will it reach the ground from its maximum height? 2 s 4 s 1 s 3 s The position x of a particle moving along x-axis is given by x = a + bt 2 where a = 8.5 m , b = 2.5 m/s 2 . Its velocity at t = 2 s is: 10 m/s 5 m/s 0 15 m/s The position x of a particle varies with time t as x = at 2 - bt 3 . The acceleration of the particle will be zero at time t equal to: a/3b a/b 2a/3b Zero A particle starts from rest and moves with constant acceleration. If the distance covered in the first 10 s is s 1 and that covered in the first 20 s is s 2 , then: s 2 = 4s 1 s 2 = 2s 1 s 2 = 3s 1 s 2 = s 1 The velocity-time graph of a body moving in a straight line is a slope of 45 with the time axis. The acceleration of the body is: 1 m/s 2 0 m/s 2 Cannot be determined 3 m/s 2 A particle moves with a velocity v = (5 i + 2 j - 3 k ) m/s under the influence of a constant acceleration a = (3 i - j + 2 k ) m/s 2 . The velocity at t=2 s is: (11 i + k ) m/s (11 i + 4 j + k ) m/s (8 i + j - k ) m/s (11 i + k ) m/s 2 An object is moving with a constant acceleration. Its velocity at t=0 is u and at t=t is v . The displacement during this time interval is: u+v 2 t v-u 2 t (u+v)t u 2+v 2 2 t A car moving at a speed of 40 km/h can be stopped by applying brakes after at least 2 m . If the same car is moving at a speed of 80 km/h , what is the minimum stopping distance? 8 m 4 m 6 m 16 m The ratio of the distances travelled by a freely falling body in the 1 st , 2 nd , 3 rd and 4 th second is: 1 : 3 : 5 : 7 1 : 2 : 3 : 4 1 : 4 : 9 : 16 1 : 1 : 1 : 1 Two stones are thrown vertically upwards with their initial velocities in the ratio 2:3 . The ratio of the maximum heights reached by them is: 4:9 2:3 √2:√3 1:1 A particle moves along a straight line such that its position is given by x = t 3 - 3t 2 + 2 metres. The velocity of the particle when its acceleration is zero is: -3 m/s 3 m/s 0 m/s -2 m/s The position x of a particle moving along the x-axis is x = 8t - 2t 2 . The maximum value of x reached by the particle is: 8 m 4 m 16 m 2 m The displacement x of a particle moving in a straight line is x = A + Bt + Ct 2 . The acceleration of the particle is: 2C C B + 2Ct 2B The velocity of a particle at an instant is 10 m/s . After 5 s , the velocity becomes 20 m/s . If the acceleration is uniform, the displacement during this interval is: 75 m 50 m 100 m 150 m The displacement-time graph of a moving particle is a parabola. This indicates that the particle is moving with: Constant acceleration Constant velocity Increasing acceleration Decreasing acceleration The position of a particle is given by x(t) = 4t 3 - 3t 2 + 2 . The instantaneous acceleration of the particle at t = 2 s is: 42 m/s 2 12 m/s 2 24 m/s 2 36 m/s 2 A stone is dropped from a tower of height h . It reaches the ground in t seconds. At what time t/3 was the stone from the ground? 8h/9 h/9 h/3 2h/3 If the velocity of a particle is given by v = 10 + 2t 2 , the average acceleration between t = 2 s and t = 5 s is: 14 m/s 2 12 m/s 2 10 m/s 2 15 m/s 2 A ball is thrown vertically up ward. It has a speed of 10m/sec when it has reached one half of its maximum height. How high does the ball rise? Take g = 10 m/s 2 - 5m 15m 10 m 20 m Two bodies, A(of mass 1kg) and B(of mass 3kg), are dropped from heights of 16 m and 25 m respectively. The ratio of the time taken by them to reach the ground is:- 5 4 12 5 5 12 4 5 A particle starts its motion from rest under the action of a constant force. If the distance covered in first 10 seconds is S 1 and that covered in the first 20 seconds is S 2 then : S 2 = S 1 S 2 = 2S 1 S 2 = 3S 1 S 2 = 4S 1 A stone falls freely under gravity. It covers distances h 1 , h 2 and h 3 in the first 5 seconds, the next 5 seconds and the next 5 seconds respectively. The relation between h 1 , h 2 and h 3 is h 1=2h 2=3h 3 h 1= h 2 3 = h 3 5 h 2=3h 1 and h 3=3h 2 h 1=h 2=h 3 A ball is thrown vertically downward with a velocity of 20 m/s from the top of a tower. It hits the ground after some time with a velocity of 80 m/s . The height of the tower is : (g = 10 m/s 2 ) 340 m 320 m 300 m 360 m A body moves from rest with constant acceleration. The ratio of distance covered in the 3 rd second to that in the 4 th second is: 5:7 3:4 9:16 1:2 The ratio of the distances travelled by a freely falling body in the 1 st , 2 nd , 3 rd and 4 th second 1 : 4 : 9 : 16 1 : 3 : 5 : 7 1 : 1 : 1 : 1 1 : 2 : 3 : 4 A horizontal bridge is built across a river. A student standing on the bridge throws a small ball vertically upwards with a velocity 4 m s -1 . The ball strikes the water surface after 4 s. The height of bridge above water surface is (Take g = 10 m s -2 ) 56 m 60 m 64 m 68 m When a ruler falls vertically, 5 different persons catch it with different reaction times. ( g = 9.8 m s -2 ) A. Person A has reaction time of 0.20 s. B. Person B has reaction time of 0.22 s. C. Person C has reaction time of 0.18 s. D. Person D has reaction time of 0.19 s. E. Person E has reaction time of 0.21 s. What is the correct order of the distance travelled by the ruler for each person? B > E > A > C > D C > D > A > E > B C > D > A > B > E B > E > A > D > C The following plots show variation of velocity (v) with time (t) of a ball thrown vertically upward, and falling back. Which of the following plots is/are correct? B only A and E only C only D only A particle moves along a straight line such that its displacement at any time t is given by s = (t 3 - 6t 2 + 3t + 4) metres. The velocity when the acceleration is zero is: -9 ms -1 3 ms -1 -12 ms -1 42 ms -1 A stone is dropped from a height h . It hits the ground with a certain momentum P . If the same stone is dropped from a height 100 % more than the previous height, the momentum when it hits the ground will change by: 41 % 68 % 100 % 200 % The position x of a particle with respect to time t along x-axis is given by x = 9t 2 - t 3 where x is in metres and t in seconds. What will be the position of this particle when it achieves maximum speed along the +x direction? 54 m 81 m 24 m 32 m A particle moves along a straight line OX . At a time t (in seconds) the distance x (in metres) of the particle from O is given by x = 40 + 12t - t 3 . How long would the particle travel before coming to rest? 16 m 24 m 40 m 56 m A stone is thrown vertically upwards. When stone is at a height half of its maximum height, its speed is 10 m/s ; then the maximum height attained by the stone is ( g=10 m/s 2 ): 10 m 8 m 15 m 20 m If a ball is thrown vertically upwards with speed u , the distance covered during the last t seconds of its ascent is: ½ gt 2 ut - ½ gt 2 (u-gt)t ut Two balls A and B are thrown with the same velocity u from the top of a tower. Ball A is thrown vertically upwards and ball B is thrown vertically downwards. If v A and v B are their respective velocities on reaching the ground, then: v A = v B v A > v B v B > v A They depend on their masses A stone is dropped from a balloon rising with acceleration a . The acceleration of the stone the relative to the ground the instant it is dropped is: g (downwards) g-a (downwards) g+a (downwards) Zero An object is thrown vertically upward with some velocity. If it passes a point at height h at time t 1 (upward) and t 2 (downward), then the value of h is: 1 2 gt 1t 2 gt 1t 2 1 8 g(t 1+t 2) 2 1 2 g(t 1+t 2) A body is moving with a constant acceleration. It covers 20 m in the 2 nd second and 30 m in the 4 th second. What is its initial velocity? 12.5 m/s 10 m/s 15 m/s 5 m/s For a particle moving under constant acceleration a , the slope of the v 2 versus displacement s graph is: 2a a a/2 ∑ a Two cars P and Q start from a point at the same time in a straight line and their positions are represented by x P(t) = at + bt 2 and x Q(t) = ft - t 2 . At what time do the cars have the same velocity? f - a 2(b + 1) a + f 2(b - 1) a + f 2(1 + b) f - a 2(b - 1) A bullet is fired into a wooden plank with a speed u . After penetrating a distance x , its speed becomes u/2 . What is the total distance it will penetrate before coming to rest, assuming constant retardation? 4x/3 2x 3x/2 5x/4 A stone is thrown vertically upwards with a velocity u . The distance travelled by it in the fifth second of its motion is equal to the distance travelled by it in the sixth second. The initial velocity u is ( g = 10 m/s 2 ): 50 m/s 100 m/s 25 m/s 40 m/s A particle moves in a straight line with deceleration a proportional to its displacement x . The loss of kinetic energy for any displacement x is proportional to: x 2 x x 3/2 x A body starts from rest and moves with a constant acceleration. The ratio of the distance covered in the n th second to the distance covered in n seconds is: (2n-1)/n 2 (2n-1)/n 1/n 2 2/n - 1/n 2 A stone is dropped from a height H . It takes t seconds to reach the ground. Where is the stone at time t/2 ? 3H/4 from the ground H/2 from the ground H/4 from the ground 2H/3 from the ground A body starts from rest and moves with uniform acceleration a . The distance covered by it in the n th second is: a(n - 1/2) a(n + 1/2) a(2n - 1)/2 an 2/2 The velocity of a particle at t=0 is 10 m/s . It moves with a constant retardation of 2 m/s 2 . The distance travelled in the 6 th second is: 1 m 0.5 m 2 m 0 m The displacement x of a particle moving in one dimension under the action of a constant force is related to time t by t = x + 3 , where x is in meters and t is in seconds. The displacement of the particle when its velocity is zero is: 0 m 3 m 6 m 9 m A body is thrown vertically up from the top of a tower with velocity 5 m/s . It reaches the ground with velocity 25 m/s . The height of the tower is ( g = 10 m/s 2 ): 30 m 25 m 20 m 35 m A balloon is rising vertically with a velocity of 10 m/s . When it is at a height of 40 m from the ground, a stone is dropped from it. The time taken by the stone to reach the ground is ( g = 10 m/s 2 ): 4 s 2 s 3 s 5 s A particle moves along a straight line with a constant acceleration. It passes through a point P with a velocity v and another point Q with a velocity 3v . The velocity of the particle at the midpoint of PQ is: 5 v 10 v 2v 2 v A car accelerates from rest at a constant rate for some time, after which it decelerates at a constant rate and comes to rest. If the total time elapsed is t , then the maximum velocity acquired by the car is: ( + )t ( 2 + 2 )t ( + )t ( 2 - 2 )t A bullet fired into a target loses half its velocity after penetrating 30 cm . At what further distance will it come to rest? 10 cm 20 cm 15 cm 30 cm A point moves with uniform acceleration a . Its initial velocity is u . The distance covered by the point in the (n+1) th second is: u + a(n + 1/2) u + a(n - 1/2) u + an u + a/2 (2n-1) A ball is dropped from a height h . If it takes t 1 to cover the first half of the distance and t 2 to cover the second half, then: t 1 = t 2( 2 + 1) t 1 = t 2 t 2 = t 1( 2 - 1) t 2 = t 1 2 A particle moves in a straight line with a velocity v given by v 2 = 2 - 3x , where x is the displacement. The acceleration of the particle is: -1.5 m/s 2 3 m/s 2 -3 m/s 2 1.5 m/s 2 The instantaneous velocity of a particle is given by v = a i + (b + ct) j . The magnitude of the acceleration of the particle is: c a 2 + b 2 a 2 + c 2 b+c The relation between time t and distance x is t = ax 2 + bx where a and b are constants. The retardation is: 2av 3 2bv 3 2av 2 2bv 2 A ball is dropped from a height h . As it bounces off the floor, its speed becomes 80 % of the speed it had just before hitting. The height to which it rises after the first bounce is: 0.64h 0.8h 0.4h 0.5h A particle moves along the x-axis such that its position is given by x = t 3 - 9t 2 + 24t + 1 . The particle comes to rest at time t equal to: 2 s and 4 s 3 s 1 s and 5 s 0 s A stone is dropped from the top of a cliff. The distance it covers in the first 3 seconds is x . In the next 3 seconds, it covers a distance y . The relation between x and y is: y = 3x y = x y = 2x y = 4x A particle moves in a straight line with a constant acceleration. It covers a distance of 12 m in the 2 nd second and 20 m in the 4 th second. The distance covered by it in the 6 th second will be: 28 m 24 m 32 m 30 m An object starts from rest and moves with a constant acceleration of 2 m/s 2 for 10 s . It then moves with constant velocity for 20 s and finally stops in 5 s with constant retardation. Total distance covered is: 550 m 500 m 600 m 400 m A particle moves such that its acceleration a is given by a = -bx , where x is the displacement from equilibrium and b is a positive constant. The period of oscillation is: 2 / b 2 b b / 2 1 / 2 b A particle moves in a straight line with retardation a proportional to its velocity v . If the initial velocity is u , the velocity after covering distance s is: u - ks u - ks 2 u e -ks u + ks A stone is dropped from a rising balloon which is at a height of 40 m and is ascending with a velocity of 10 m/s . After how many seconds does the stone hit the ground? ( g = 10 m/s 2 ) 4 s 2 s 3 s 8 s A particle moves such that its acceleration a is given by a = -kx where x is displacement and k is a positive constant. The velocity of the particle when its displacement is x is (initial velocity u=0 at x=x 0 ): k(x 0 2 - x 2) k(x 2 - x 0 2) k(x 0 - x) 1 2 kx 2 A stone is thrown horizontally from a height h with velocity v . Another stone is dropped from the same height. The time taken by the two stones to reach the ground is: Equal Dependent on v More for the thrown stone Less for the thrown stone A stone is thrown vertically upward with a speed v . It passes a point P at height h after t 1 seconds and again after t 2 seconds while coming down. The value of v is: 1 2 g(t 1 + t 2) g(t 1 + t 2) gt 1 t 2 1 2 g(t 2 - t 1) A particle moves along the x-axis with an acceleration a = 2x . If it starts from rest at x = 1 m , find its velocity when it reaches x = 3 m . 4 m/s 2 2 m/s 8 m/s 16 m/s A particle moves along a straight line with an acceleration a = 6t + 4 . If its initial velocity is 2 m/s at t=0 , what is its velocity at t=3 s ? 41 m/s 31 m/s 29 m/s 39 m/s A small block slides down on a smooth inclined plane, starting from rest at time t = 0 . Let S n be the distance travelled by the block in the interval t = n-1 to t = n . Then, the ratio S n S n+1 is: 2n-1 2n+1 2n+1 2n-1 n n+1 2n 2n-1 A stone is dropped from a height h . Simultaneously, another stone is thrown up from the ground with such a velocity that it can reach a maximum height h . The time at which they pass each other is: h 2g 2h g h g h 2g The velocity of a particle is v = v 0 + gt + ft 2 . If its position is x = 0 at t = 0 , then its displacement after time t = 1 s is: v 0 + g/2 + f/3 v 0 + g + f v 0 + g/2 + f g + 2f A body moves from rest with uniform acceleration. If it travels a distance x in the first 2 seconds and y in the next 2 seconds, then: y = 3x y = x y = 2x y = 4x A body is projected vertically upwards. If t 1 and t 2 are the times at which it is at height h while ascending and descending respectively, then the initial velocity u is: 1 2 g(t 1 + t 2) g(t 1 + t 2) 1 2 g t 1 t 2 gt 1 t 2 A car accelerates from rest at 2 m/s 2 for 10 s and then retards at 4 m/s 2 to come to rest. The total distance covered is: 150 m 100 m 200 m 300 m A particle moves in a straight line such that its velocity v at any displacement x is given by v 2 = a - bx . The acceleration of the particle is: -b/2 -b a/2 b/2 The ratio of distances traveled by a body starting from rest and moving with uniform acceleration in the first, second and third second is: 1 : 3 : 5 1 : 2 : 3 1 : 4 : 9 1 : 2 : 3 A toy car with charge q moves on a frictionless horizontal plane surface under the influence of a uniform electric field E . Due to the force q E , its velocity increases from 0 to 6 m/s in one second duration. At that instant the direction of the field is reversed. The car continues to move for two more seconds under the influence of this field. The average velocity and the average speed of the toy car between 0 to 3 seconds are respectively 1 m/s, 3.5 m/s 1 m/s, 3 m/s 2 m/s, 4 m/s 1.5 m/s, 3 m/s When an object is shot from the bottom of a long smooth inclined plane kept at an angle 60 with horizontal, it can travel a distance x 1 along the plane. But when the inclination is decreased to 30 and the same object is shot with the same velocity, it can travel x 2 distance. Then x 1 : x 2 will be: 1 : 2 3 1 : 2 2 : 1 1 : 3 A small block slides down on a smooth inclined plane, starting from rest at time t = 0 . Let S n be the distance travelled by the block in the interval t = n - 1 to t = n . Then, the ratio S n S n+1 is 2n-1 2n+1 2n+1 2n-1 2n 2n-1 2n-1 2n A bullet from a gun is fired on a rectangular wooden block with velocity u . When bullet travels 24 cm through the block along its length horizontally, velocity of bullet becomes u 3 . Then it further penetrates into the block in the same direction before coming to rest exactly at the other end of the block. The total length of the block is 27 cm 24 cm 28 cm 30 cm A person sitting in the ground floor of a building notices through the window, of height 1.5 m , a ball dropped from the roof of the building crosses the window in 0.1 s . What is the velocity of the ball when it is at the topmost point of the window? ( g = 10 m/s 2 ) 14.5 m/s 15.5 m/s 20 m/s 4.5 m/s A particle moves a distance x in time t according to equation x = (t+5) -1 . The acceleration of particle is proportional to: ( velocity ) 3/2 ( distance ) 2 ( distance ) -2 ( velocity ) 2/3 A particle moves with constant acceleration and v 1, v 2 and v 3 are its average velocities in the three successive intervals t 1, t 2 and t 3 of time. Then which of the following is correct? (v 1 - v 2) / (v 2 - v 3) = (t 1 + t 2) / (t 2 + t 3) (v 1 - v 2) / (v 2 - v 3) = (t 1 - t 2) / (t 2 - t 3) (v 1 - v 2) / (v 2 - v 3) = t 1 / t 3 (v 1 - v 2) / (v 2 - v 3) = (t 2 - t 1) / (t 3 - t 2) A ball is dropped from a bridge 122.5 m above a river. After the ball has been falling for 2 s , a second ball is thrown straight down after it. What must its initial velocity be so that both hit the water at the same time? 26.1 m/s 9.8 m/s 55.5 m/s 40 m/s A point moves with uniform acceleration and v 1, v 2, v 3 denote the average velocities in the three successive intervals of time t 1, t 2, t 3 . Which of the following relations is correct? v 1 - v 2 v 2 - v 3 = t 1 + t 2 t 2 + t 3 v 1 - v 2 v 2 - v 3 = t 1 - t 2 t 2 - t 3 v 1 - v 2 = v 2 - v 3 v 1 - v 2 v 2 - v 3 = t 1 t 3 The time taken by a particle to come to rest, if its retardation is given by a = -kv 2 (where k is a constant and v is instantaneous velocity), is proportional to: 1/v 0 v 0 v 0 2 Independent of v 0