Title 03. Motion in a Staright line Easy.pdf ✅

1. A Body moves 6 m north. 8 m east and 10m vertically upwards, what is its resultant displacement from initial position (a) 10 2m (b) 10m (c) m 2 10 (d) 10  2m 2. A man goes 10m towards North, then 20m towards east then displacement is (a) 22.5m (b) 25m (c) 25.5m (d) 30m 3. A person moves 30 m north and then 20 m towards east and finally 30 2 m in south-west direction. The displacement of the person from the origin will be (a) 10 m along north (b) 10 m long south (c) 10 m along west (d) Zero 4. An aeroplane flies 400 m north and 300 m south and then flies 1200 m upwards then net displacement is (a) 1200 m (b) 1300 m (c) 1400 m (d) 1500 m 5. An athlete completes one round of a circular track of radius R in 40 sec. What will be his displacement at the end of 2 min. 20 sec (a) Zero (b) 2R (c) 2R (d) 7R 6. A wheel of radius 1 meter rolls forward half a revolution on a horizontal ground. The magnitude of the displacement of the point of the wheel initially in contact with the ground is (a) 2 (b) 2 (c) 4 2  + (d)  7. A person travels along a straight road for half the distance with velocity 1 v and the remaining half distance with velocity 2 v The average velocity is given by (a) 1 2 v v (b) 2 1 2 2 v v (c) 2 1 2 v + v (d) 1 2 1 2 2 v v v v + 8. The displacement-time graph for two particles A and B are straight lines inclined at angles of o 30 and o 60 with the time axis. The ratio of velocities of VA VB : is (a) 1 : 2 (b) 1 : 3 (c) 3 : 1 (d) 1 : 3 9. A car travels from A to B at a speed of 20 km / hr and returns at a speed of 30 km / hr . The average speed of the car for the whole journey is (a) 25 km / hr (b) 24 km / hr (c) 50 km / hr (d) 5 km / hr 10. A boy walks to his school at a distance of 6 km with constant speed of 2.5 km/hour and walks back with a constant speed of 4 km/hr. His average speed for round trip expressed in km/hour, is (a) 24/13 (b) 40/13 (c) 3 (d) 1/2 11. A car travels the first half of a distance between two places at a speed of 30 km/hr and the second half of the distance at 50 km/hr. The average speed of the car for the whole journey is (a) 42.5 km/hr (b) 40.0 km/hr (c) 37.5 km/hr (d) 35.0 km/hr 12. One car moving on a straight road covers one third of the distance with 20 km/hr and the rest with 60 km/hr. The average speed is (a) 40 km/hr (b) 80 km/hr (c) 3 2 46 km/hr (d) 36 km/hr 13. A car moves for half of its time at 80 km/h and for rest half of time at 40 km/h. Total distance covered is 60 km. What is the average speed of the car (a) 60 km / h (b) 80 km / h (c) 120 km / h (d) 180 km / h 14. A train has a speed of 60 km/h. for the first one hour and 40 km/h for the next half hour. Its average speed in km/h is (a) 50 (b) 53.33 (c) 48 (d) 70 15. Which of the following is a one dimensional motion (a) Landing of an aircraft (b) Earth revolving a round the sun (c) Motion of wheels of a moving trains (d)Train running on a straight track 16. A 150 m long train is moving with a uniform velocity of 45 km/h. The time taken by the train to cross a bridge of length 850 meters is (a) 56 sec (b) 68 sec (c) 80 sec (d) 92 sec 17. A particle is constrained to move on a straight line path. It returns to the starting point after 10 sec. The total distance covered by the particle during this time is 30 m. Which of the following statements about the motion of the particle is false (a) Displacement of the particle is zero (b)Average speed of the particle is 3 m/s
(c) Displacement of the particle is 30 m (d)Both (a) and (b) 18. A particle moves along a semicircle of radius 10m in 5 seconds. The average velocity of the particle is (a) 1 2 −  ms (b) 1 4 −  ms (c) 1 2 − ms (d) 1 4 − ms 19. A man walks on a straight road from his home to a market 2.5 km away with a speed of 5 km/h. Finding the market closed, he instantly turns and walks back home with a speed of 7.5 km/h. The average speed of the man over the interval of time 0 to 40 min. is equal to (a) 5 km/h (b) 4 25 km/h (c) 4 30 km/h (d) 8 45 km/h 20. The ratio of the numerical values of the average velocity and average speed of a body is always (a) Unity (b) Unity or less (c) Unity or more (d) Less than unity 21. A person travels along a straight road for the first half time with a velocity 1 v and the next half time with a velocity 2 v . The mean velocity V of the man is (a) 1 2 2 1 1 V v v = + (b) 2 1 2 v v V + = (c) 1 2 V = v v (d) 2 1 v v V = 22. Which of the following options is correct for the object having a straight line motion represented by the following graph (a) The object moves with constantly increasing velocity from O to A and then it moves with constant velocity. (b) Velocity of the object increases uniformly (c) Average velocity is zero (d) The graph shown is impossible 23. The numerical ratio of displacement to the distance covered is always (a) Less than one (b)Equal to one (c) Equal to or less than one (d)Equal to or greater than one 24. A 100 m long train is moving with a uniform velocity of 45 km/hr. The time taken by the train to cross a bridge of length 1 km is (a) 58 s (b) 68 s (c) 78 s (d) 88 s 25. A particle moves for 20 seconds with velocity 3 m/s and then velocity 4 m/s for another 20 seconds and finally moves with velocity 5 m/s for next 20 seconds. What is the average velocity of the particle (a) 3 m/s (b) 4 m/s (c) 5 m/s (d) Zero 26. The correct statement from the following is (a) A body having zero velocity will not necessarily have zero acceleration (b) A body having zero velocity will necessarily have zero acceleration (c) A body having uniform speed can have only uniform acceleration (d) A body having non-uniform velocity will have zero acceleration 27. Two boys are standing at the ends A and B of a ground where AB = a . The boy at B starts running in a direction perpendicular to AB with velocity . 1 v The boy at A starts running simultaneously with velocity v and catches the other boy in a time t, where t is (a) 2 1 2 a / v + v (b) /( ) 2 1 2 2 a v − v (c) /( )1 a v − v (d) /( )1 a v + v 28. A car travels half the distance with constant velocity of 40 kmph and the remaining half with a constant velocity of 60 kmph. The average velocity of the car in kmph is (a) 40 (b) 45 (c) 48 (d) 50 29. A particle experiences a constant acceleration for 20 sec after starting from rest. If it travels a distance 1 S in the first 10 sec and a distance 2 S in the next 10 sec, then (a) 1 2 S = S (b) / 3 1 2 S = S (c) / 2 1 2 S = S (d) / 4 1 2 S = S 30. The displacement x of a particle along a straight line at time t is given by 2 0 1 2 x = a + a t + a t . The acceleration of the particle is (a) 0 a (b) 1 a (c) 2 2a (d) 2 a s t D C B A O
31. The coordinates of a moving particle at any time are given by 2 x = at and 2 y = bt . The speed of the particle at any moment is (a) 2t(a + b) (b) 2 ( ) 2 2 t a − b (c) 2 2 t a + b (d) 2 ( ) 2 2 t a + b 32. An electron starting from rest has a velocity that increases linearly with the time that is v = kt, where 2 k = 2m /sec . The distance travelled in the first 3 seconds will be (a) 9 m (b) 16 m (c) 27 m (d) 36 m 33. The displacement of a body is given to be proportional to the cube of time elapsed. The magnitude of the acceleration of the body is (a) Increasing with time (b) Decreasing with time (c) Constant but not zero (d) Zero 34. A body is moving from rest under constant acceleration and let 1 S be the displacement in the first (p − 1) sec and 2 S be the displacement in the first p sec. The displacement in th (p p 1) 2 − + sec. will be (a) 1 2 S + S (b) 1 2 S S (c) 1 2 S − S (d) 1 2 S / S 35. A body under the action of several forces will have zero acceleration (a) When the body is very light (b) When the body is very heavy (c) When the body is a point body (d) When the vector sum of all the forces acting on it is zero 36. A body starts from the origin and moves along the X-axis such that the velocity at any instant is given by (4 2 ) 3 t − t , where t is in sec and velocity in m / s . What is the acceleration of the particle, when it is 2 m from the origin (a) 2 28 m /s (b) 2 22 m / s (c) 2 12 m / s (d) 2 10 m / s 37. The relation between time and distance is t = x + x 2 , where  and  are constants. The retardation is (a) 3 2v (b) 3 2v (c) 3 2v (d) 2 3 2 v 38. A point moves with uniform acceleration and 1 2 v ,v and 3 v denote the average velocities in the three successive intervals of time 1 2 t , t and 3 t . Which of the following relations is correct (a) ( ):( ) ( ):( ) 1 2 2 3 1 2 2 3 v − v v − v = t − t t + t (b) ( ):( ) ( ):( ) 1 2 2 3 1 2 2 3 v − v v − v = t + t t + t (c) ( ):( ) ( ):( ) 1 2 2 3 1 2 1 3 v − v v − v = t − t t − t (d) ( ):( ) ( ):( ) 1 2 2 3 1 2 2 3 v − v v − v = t − t t − t 39. The acceleration of a moving body can be found from (a) Area under velocity-time graph (b)Area under distance-time graph (c) Slope of the velocity-time graph (d)Slope of distance-time graph 40. The initial velocity of a particle is u (at t = 0 ) and the acceleration f is given by at . Which of the following relation is valid (a) 2 v = u + at (b) 2 2 t v = u + a (c) v = u + at (d) v = u 41. The initial velocity of the particle is 10 m / sec and its retardation is 2 2m /sec . The distance moved by the particle in 5th second of its motion is (a) 1 m (b) 19 m (c) 50 m (d) 75 m 42. A motor car moving with a uniform speed of 20 m /sec comes to stop on the application of brakes after travelling a distance of 10 m Its acceleration is (a) 2 20 m / sec (b) 2 − 20m / sec (c) 2 − 40 m /sec (d) 2 + 2m /sec 43. The velocity of a body moving with a uniform acceleration of 2 2 m. / sec is 10 m / sec . Its velocity after an interval of 4 sec is (a) 12 m / sec (b) 14 m / sec (c) 16 m / sec (d) 18 m / sec 44. A particle starting from rest travels a distance x in first 2 seconds and a distance y in next two seconds, then (a) y = x (b) y = 2x (c) y = 3 x (d) y = 4 x 45. The initial velocity of a body moving along a straight line is 7 m / s . It has a uniform acceleration of 2 4 m / s . The distance covered by the body in the 5th second of its motion is (a) 25 m (b) 35 m (c) 50 m (d) 85 m 46. The velocity of a body depends on time according to the equation 2 v = 20 + 0.1t . The body is undergoing (a) Uniform acceleration (b) Uniform retardation
(c) Non-uniform acceleration (d) Zero acceleration 47. Which of the following four statements is false (a) A body can have zero velocity and still be accelerated (b) A body can have a constant velocity and still have a varying speed (c) A body can have a constant speed and still have a varying velocity (d) The direction of the velocity of a body can change when its acceleration is constant 48. A particle moving with a uniform acceleration travels 24 m and 64 m in the first two consecutive intervals of 4 sec each. Its initial velocity is (a) 1 m/sec (b) 10 m / sec (c) 5 m/sec (d) 2 m/sec 49. The position of a particle moving in the xy-plane at any time t is given by (3 6 ) 2 x = t − t metres, ( 2 ) 2 y = t − t metres. Select the correct statement about the moving particle from the following (a) The acceleration of the particle is zero at t = 0 second (b) The velocity of the particle is zero at t = 0 second (c) The velocity of the particle is zero at t =1 second (d) The velocity and acceleration of the particle are never zero 50. If body having initial velocity zero is moving with uniform acceleration 2 8 m / sec the distance travelled by it in fifth second will be (a) 36 metres (b) 40 metres (c) 100 metres (d) Zero 51. An alpha particle enters a hollow tube of 4 m length with an initial speed of 1 km/s. It is accelerated in the tube and comes out of it with a speed of 9 km/s. The time for which it remains inside the tube is (a) 3 8 10 −  s (b) s 3 80 10 −  (c) s 3 800 10 −  (d) s 4 8 10 −  52. A body of mass 10 kg is moving with a constant velocity of 10 m/s. When a constant force acts for 4 seconds on it, it moves with a velocity 2 m/sec in the opposite direction. The acceleration produced in it is (a) 2 3 m / sec (b) 2 − 3m /sec (c) 2 0.3 m /sec (d) 2 − 0.3m /sec 53. A body starts from rest from the origin with an acceleration of 2 6 m / s along the x-axis and 2 8 m / s along the y-axis. Its distance from the origin after 4 seconds will be (a) 56 m (b) 64 m (c) 80 m (d) 128 m 54. A car moving with a velocity of 10 m/s can be stopped by the application of a constant force F in a distance of 20 m. If the velocity of the car is 30 m/s, it can be stopped by this force in (a) m 3 20 (b) 20 m (c) 60 m (d) 180 m 55. The displacement of a particle is given by 2 4 y = a + bt + ct − dt . The initial velocity and acceleration are respectively (a) b, − 4d (b) −b, 2c (c) b, 2c (d) 2c, − 4d 56. A car moving with a speed of 40 km/h can be stopped by applying brakes after atleast 2 m. If the same car is moving with a speed of 80 km/h, what is the minimum stopping distance (a) 8 m (b) 2 m (c) 4 m (d) 6 m 57. An elevator car, whose floor to ceiling distance is equal to 2.7 m, starts ascending with constant acceleration of 1.2 ms–2 . 2 sec after the start, a bolt begins fallings from the ceiling of the car. The free fall time of the bolt is (a) 0.54 s (b) 6 s (c) 0.7 s (d) 1 s 58. The displacement is given by 2 5 2 x = t + t + , the acceleration at t = 2s is (a) 2 4 m / s (b) 2 8 m / s (c) 2 10 m / s (d) 2 15 m / s 59. Two trains travelling on the same track are approaching each other with equal speeds of 40 m/s. The drivers of the trains begin to decelerate simultaneously when they are just 2.0 km apart. Assuming the decelerations to be uniform and equal, the value of the deceleration to barely avoid collision should be (a) 11.8 2 m / s (b) 11.0 2 m / s (c) 2.1 2 m / s (d) 0.8 2 m / s 60. A body moves from rest with a constant acceleration of 2 5 m / s . Its instantaneous speed (in m / s) at the end of 10 sec is (a) 50 (b) 5 (c) 2 (d) 0.5 61. A boggy of uniformly moving train is suddenly detached from train and stops after covering some distance. The distance covered by the boggy and distance covered by the train in the same time has relation (a) Both will be equal (b)First will be half of second (c) First will be 1/4 of second (d)No definite ratio