Frame of Reference & Motion 1D — Practice Questions

Free NEET Physics multiple-choice questions on Frame of Reference & Motion 1D. Attempt each question and reveal the answer with a full explanation.

Which of the following displacement-time graphs is not possible for a real particle moving in a straight line? A vertical straight line A horizontal straight line A straight line with positive slope A downward opening parabola Which of the following graphs represents the variation of acceleration a with displacement x for a particle falling freely under gravity? A horizontal line parallel to the x-axis A straight line passing through origin with positive slope A straight line passing through origin with negative slope A parabola 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 unit time ( t = 1 ) is: v 0 + g/2 + f/3 v 0 + g + f v 0 + g/2 + f v 0 + 2g + 3f The position of a particle is given by r = (3t i + 2t 2 j + 8 k ) m. The velocity v of the particle at t = 2 s is: (3 i + 8 j ) m/s (3 i + 4 j ) m/s (6 i + 8 j ) m/s (3 i + 2 j ) m/s The ratio of displacement to distance for a moving particle is: Always 1 Always = 1 Always > 1 Always 1 Which of the following graphs represents the relationship between the distance s and time t for a particle starting from rest and moving with a constant acceleration? A parabola opening upwards A straight line passing through the origin A parabola opening towards the time axis A rectangular hyperbola A car moves from X to Y with a uniform speed v u and returns to Y with a uniform speed v d . The average speed for this round trip is: 2v uv d v u + v d v uv d v uv d v u + v d v u + v d 2 Two bodies A (of mass 1 kg ) and B (of mass 3 kg ) are dropped from heights of 16 m and 25 m , respectively. The ratio of the time taken by them to reach the ground is: 4/5 5/4 12/5 5/12 A bullet is fired from a height of 4.9 m in horizontal direction with a velocity of 9.8 m/s . The time taken by the bullet to reach the ground is: 1 s 2 s 0.5 s 9.8 s What is the linear velocity of a point on the equator of earth? (Radius of earth = R , period of rotation = T ) 2πR/T πR/T 4πR/T Zero A car covers the first half of the distance between two places at 40 km/h and another half of the distance at 60 km/h . The average speed of the car is: 48 km/h 50 km/h 45 km/h 52 km/h A car travels the first 1/4 of distance with 10 km/h , the next 1/4 with 20 km/h and the remaining half distance with 40 km/h . The average speed of the car is: 20 km/h 15 km/h 25 km/h 22.5 km/h The displacement of a particle is given by y = a + bt + ct 2 - dt 4 . The initial velocity and acceleration are: b, 2c b, c a, b 2c, -4d A car moves a distance x with a speed v 1 and then the next distance x with a speed v 2 . The average speed is: 2v 1v 2 v 1 + v 2 v 1 + v 2 2 v 1 + v 2 v 1v 2 v 1v 2 The displacement-time graph for two particles A and B are straight lines inclined at angles of 30 and 60 with the time axis. The ratio of velocity of A to velocity of B is: 1:3 1: 3 3 :1 3:1 The area under the acceleration-time graph for a particle represents: Change in velocity Displacement Distance travelled Final velocity The speed-time graph of a particle is a straight line passing through the origin with a positive slope. The distance-time graph will be: A parabola opening upwards A straight line through the origin A circle A parabola opening downwards The area under the velocity-time graph for a particle represents: Displacement Acceleration Force Momentum The displacement-time graph of two moving particles make angles of 30 and 45 with the time-axis. The ratio of their velocities is: 1 : √3 1 : 2 1 : 1 √3 : 1 A car moves from X to Y with a uniform speed v u and returns to Y with a uniform speed v d . The average speed for this round trip is v u v d v d v u v d + v u v u + v d 2 2v d v u v d + v u . A bus is moving with a speed of 10 ms -1 on a straight road. A scooterist wishes to overtake the bus in 100s. If the bus is at a distance of 1 km from the scooterist, with what speed should the scooterist chase the bus ? 10 ms -1 20 ms -1 40 ms -1 25 ms -1 If the velocity of a particle is v = At + Bt 2 , where A and B are constants, then the distance travelled by it between 1s and 2s is :- 3 2 A + 4B 3A + 7B 3 2 A + 7 3 B A 2 + B 3 The displacement of a particle is given by x = (t-3) 2 where x is in meters and t is in seconds. The velocity of the particle at t=3 s is: 0 m/s 3 m/s -3 m/s 6 m/s The displacement-time graphs of two moving particles make angles of 30 and 45 with the x -axis as shown in the figure. The ratio of their respective velocity is 1 : 1 1 : 2 1 : 3 3 : 1 A vehicle travels half the distance with speed v and the remaining distance with speed 2v . Its average speed is v 3 2v 3 4v 3 3v 4 Which of the following speed-time graphs represents the motion of an object thrown vertically upwards and then returning to the thrower's hand? (Assume no air resistance) V-shaped graph touching the time axis A straight line parallel to time axis A downward sloping straight line through origin A parabolic curve opening upwards The velocity-time graph of a particle moving in a straight line is shown in the figure. The total distance travelled by the particle in 10 s is: 100 m 50 m 0 m 80 m The acceleration of a particle is increasing linearly with time t as bt . The particle starts from the origin with an initial velocity v 0 . The distance travelled by the particle in time t will be: v 0t + 1 6 bt 3 v 0t + 1 3 bt 3 v 0t + 1 2 bt 2 v 0t + bt 2 A particle moves along a straight line such that its displacement x at any time t is given by t = x + 3 , where x is in metres and t is in seconds. The displacement of the particle when its velocity is zero is: 0 m 3 m 9 m 1 m The velocity-time graph of a particle is shown. The ratio of the distance to the displacement of the particle in 4 seconds is: 3:1 2:1 1:1 4:3 The velocity of a particle moving along the x-axis is given by v = k x , where k is a positive constant. The acceleration of the particle is: k 2/2 k 2 k/2 2k 2 The position x of a particle moving in a straight line depends on time t as x = at 3 + bt 2 + ct + d . The ratio of its initial velocity to its initial acceleration is: c/2b c/b c/3a b/2c The position of a particle is given by x = 2(t - t 2) where t is in seconds and x is in metres. The maximum value of position x is: 0.5 m 1 m 2 m 0.25 m The speed-time graph of a particle is shown in the figure. The distance travelled by the particle between t=0 to t=10 s is: 100 m 50 m 200 m 10 m The position of a particle is given by x = (t-2) 2 where x is in meters and t is in seconds. The distance travelled by the particle in the first 4 seconds is: 8 m 0 m 4 m 16 m A car travels 1/3 of the total distance with speed 10 km/h , the next 1/3 with 20 km/h and the last 1/3 with 60 km/h . The average speed of the car is: 18 km/h 30 km/h 25 km/h 36 km/h If the velocity of a particle is given by v = x , where x is the displacement, then the acceleration of the particle is: 0.5 m/s 2 1 m/s 2 2 m/s 2 v m/s 2 The velocity-time graph of a particle is given by a straight line passing through the origin and making an angle of 30 with the time axis. The displacement of the particle in 2 s is: 2 3 m 3 m 1 3 m 2 3 m The displacement x of a particle moving in a straight line is given by x = 16t - 2t 2 (where x is in meters and t is in seconds). The distance travelled by the particle in 8 seconds is: 64 m 32 m 0 m 128 m The position of a particle is given by x(t) = (t 3 - 6t 2 + 9t + 5) m . The distance travelled by the particle in the first 4 seconds is: 6 m 4 m 2 m 8 m A particle moves with a constant speed v along a square of side L . The magnitude of average velocity when the particle moves from one corner to the diagonally opposite corner is: v 2 v 2 v 2v The position of a particle is given by x = At 2 and y = Bt 2 . The trajectory of the particle is a: Straight line Parabola Circle Ellipse A particle moves along the x -axis with velocity v = f(x) . The acceleration of the particle is: f(x) f'(x) f'(x) f 2(x) f(x)/x A particle moves along a straight line with a velocity v = v 0(1 - t T ) where v 0 and T are constants. The total distance travelled by the particle until it stops is: 1 2 v 0 T v 0 T 1 3 v 0 T 2v 0 T The velocity-time graph of an object moving along a straight line is shown. The net displacement of the object in 6 seconds is: 8 m 12 m 16 m 4 m The position of a particle is given by r = (t 2 - 1) i + (2t) j . The equation of its trajectory is: y 2 = 4(x+1) y = 2x + 1 x 2 + y 2 = 1 y = x 2 If a particle moves with a velocity v = (3t 2 - 6t) i m/s, the distance travelled by the particle in the first 3 seconds is: 8 m 0 m 4 m 12 m The displacement of a particle is given by x = (t-2) 2 . The distance covered by the particle in the first 3 seconds is: 5 m 1 m 2 m 4 m The displacement x of a particle varies with time t as x = ae - t + be t , where a , b, and are positive constants. The velocity of the particle will - Be independent of and Go on increasing with time Drop to zero when = Go on decreasing with time 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: - 24 m 40 m 56 m 16 m 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 second. What will be the position of this particle when it achieves maximum speed along the +ve x direction? 54m 81m 24m 32m. A particle moving along x-axis has acceleration f, at time t, given by f = f 0 (1 - t T ) , where f 0 and T are constants. The particle at t = 0 has zero velocity. In the time interval between t = 0 and the instant when f = 0 , the particle's velocity (v x) is 1 2 f 0T 2 f 0T 2 1 2 f 0T f 0T . The velocity (v) – time (t) plot of the motion of a body is shown below: The acceleration (a) – time (t) graph that best suits this motion is : In some appropriate units, time (t) and position (x) relation of a moving particle is given by t = x 2 + x . The acceleration of the particle is + 2 2x+1 - 2 (x+2) 3 - 2 (2x+1) 3 + 2 (x+1) 3 Two cities X and Y are connected by a regular bus service with a bus leaving in either direction every T min. A girl is driving scooty with a speed of 60 km/h in the direction X to Y notices that a bus goes past her every 30 minutes in the direction of her motion, and every 10 minutes in the opposite direction. Choose the correct option for the period T of the bus service and the speed (assumed constant) of the buses. 15 min, 120 km/h 9 min, 40 km/h 25 min, 100 km/h 10 min, 90 km/h A person is standing on an open car moving with constant velocity 10 m/s . He throws a ball vertically upward (relative to himself) with speed 20 m/s . The time after which the ball returns to his hand is ( g = 10 m/s 2 ): 4 s 2 s 1 s 8 s The displacement x of a particle varies with time t as x = ae -αt + be βt , where a, b, α, β are positive constants. The velocity of the particle will: go on increasing with time be independent of β drop to zero when α = β go on decreasing with time The distance travelled by a particle starting from rest and moving with an acceleration a = (4/3)t in the third second is: 19/9 m 10/3 m 6 m 4 m A particle moves along a straight line such that its velocity v varies with displacement x as v = x -2n , where and n are constants. The acceleration of the particle as a function of x is given by: -2n 2 x -4n-1 -2n 2 x -2n-1 -2n 2 x -4n+1 -2n 2 x -n-1 If the velocity of a particle is v = v 0 e -kt , the total distance traveled by the particle before it comes to rest is: v 0 / k v 0 k v 0 / k 2 Infinite If a particle moves with a velocity v(t) = 3t 2 - 6t , the distance covered by the particle in the first 3 seconds is: 8 m 0 m 4 m 12 m The position of a particle is given by x = 4(t - t 2) where x is in meters and t is in seconds. The distance travelled by the particle in the first 2 seconds is: 10 m 0 m 4 m 8 m If the velocity of a particle is given by v = (t 2 - t) m/s , the total distance travelled by the particle in the first 2 seconds is: 1 m 2/3 m 5/6 m 4/3 m A particle moves in a straight line such that its velocity is v = (3t 2 - 6t) m/s. The distance covered by the particle in the first 3 seconds is: 8 m 0 m 4 m 12 m The velocity of a particle moving in a straight line is given by v = v 0 e -kt . The distance it travels before coming to rest is: v 0 / k v 0 k k / v 0 Infinity A particle moves along a straight line such that its displacement x at any time t is given by x 2 = t 2 + 1 . The acceleration of the particle is: 1/x 3 1/x 2 -1/x 2 x 3 The position x of a particle moving along the x -axis at time t is given by x = 2t 2 - 3t + 1 . The average velocity between t=1 s and t=2 s is: 3 m/s 1 m/s 5 m/s 2 m/s Which of the following graphs cannot represent one-dimensional motion of a particle? A graph showing two different positions at the same time A straight line velocity-time graph A parabola in displacement-time graph A graph showing speed decreasing with time Consider the acceleration-time graph of a particle. The area under the curve between t 1 and t 2 represents: Change in velocity Average velocity Total distance Instantaneous speed