Tiêu đề 03. Motion in a Staright line Hard.pdf ✅

03. MOTION in a STRIGHT LINE [Hard] 1. A 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) km /hr 3 2 46 (d) 36 km/hr 2. The displacement of a particle, moving in a straight line, is given by 2 2 4 2 s = t + t + where s is in metres and t in seconds. The acceleration of the particle is (a) 2 m/s2 (b) 4 m/s2 (c) 6 m/s2 (d) 8 m/s2 3. The position x of a particle varies with time t as . 2 3 x = at − bt The acceleration of the particle will be zero at time t equal to (a) b a (b) b a 3 2 (c) b a 3 (d) Zero 4. The displacement of the 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 5. The relation between time t and distance x is , 2 t =  x + x where  and  are constants. The retardation is (v is the velocity) (a) 3 2v (b) 3 2v (c) 3 2v (d) 2 3 2 v 6. If displacement of a particle is directly proportional to the square of time. Then particle is moving with (a) Uniform acceleration (b) Variable acceleration (c) Uniform velocity (d) Variable acceleration but uniform velocity 7. A particle is moving eastwards with velocity of 5 m/s. In 10 sec the velocity changes to 5 m/s northwards. The average acceleration in this time is (a) Zero (b) 2 m/s 2 1 toward north-west (c) 2 m/s 2 1 toward north-east (d) 2 m/s 2 1 toward north-west 8. A body starts from the origin and moves along the x-axis such that velocity at any instant is given by (4 2 ) 3 t − t , where t is in second and velocity is in m/s. What is the acceleration of the particle, when it is 2m from the origin? (a) 2 28 m/s (b) 2 22 m/s (c) 2 12 m/s (d) 2 10 m/s 9. A body of mass 10 kg is moving with a constant velocity of 10 m/s. When a constant force acts for 4 sec on it, it moves with a velocity 2 m/sec in the opposite direction. The acceleration produced in it is (a) 2 3 m/s (b) 2 − 3 m/s (c) 2 0.3 m/s (d) 2 − 0.3 m/s 10. The average velocity of a body moving with uniform acceleration travelling a distance of 3.06 m is 0.34 ms–1 . If the change in velocity of the body is 0.18ms–1 during this time, its uniform acceleration is (a) 0.01 ms–2 (b) 0.02 ms–2 (c) 0.03 ms–2 (d) 0.04 ms–2 11. A particle travels 10m in first 5 sec and 10m in next 3 sec. Assuming constant acceleration what is the distance travelled in next 2 sec (a) 8.3 m (b) 9.3 m (c) 10.3 m (d) None of above 12. A body travels for 15 sec starting from rest with constant acceleration. If it travels distances 1 2 S , S and 3 S in the first five seconds, second five seconds and next five seconds respectively the relation between 1 2 S , S and 3 S is (a) 1 2 3 S = S = S (b) 1 2 3 5S = 3S = S (c) 1 2 3 5 1 3 1 S = S = S (d) 1 2 3 3 1 5 1 S = S = S 13. If a body having initial velocity zero is moving with uniform acceleration 8 / sec , 2 m the distance travelled by it in fifth second will be (a) 36 metres (b) 40 metres (c) 100 metres (d) Zero 14. The engine of a car produces acceleration 4m/sec2 in the car, if this car pulls another car of same mass, what will be the acceleration produced
(a) 8 m/s2 (b) 2 m/s2 (c) 4 m/s2 (d) 2 / 2 1 m s 15. A body starts from rest. What is the ratio of the distance travelled by the body during the 4th and 3rdsecond. (a) 7/5 (b) 5/7 (c) 7/3 (d) 3/7 16. If a body is thrown up with the velocity of 15 m/s then maximum height attained by the body is (g = 10 m/s2 ) (a) 11.25 m (b) 16.2 m (c) 24.5 m (d) 7.62 m 17. A man drops a ball downside from the roof of a tower of height 400 meters. At the same time another ball is thrown upside with a velocity 50 meter/sec. from the surface of the tower, then they will meet at which height from the surface of the tower (a) 100 meters (b) 320 meters (c) 80 meters (d) 240 meters 18. A very large number of balls are thrown vertically upwards in quick succession in such a way that the next ball is thrown when the previous one is at the maximum height. If the maximum height is 5m, the number of ball thrown per minute is (take 2 10 − g = ms ) (a) 120 (b) 80 (c) 60 (d) 40 19. A particle is thrown vertically upwards. If its velocity at half of the maximum height is 10 m/s, then maximum height attained by it is (Take g = 10 m/s2 ) (a) 8 m (b) 10 m (c) 12 m (d) 16 m 20. A stone is shot straight upward with a speed of 20 m/sec from a tower 200 m high. The speed with which it strikes the ground is approximately (a) 60 m/sec (b) 65 m/sec (c) 70 m/sec (d) 75 m/sec 21. A body freely falling from the rest has a velocity ‘v’ after it falls through a height ‘h’. The distance it has to fall down for its velocity to become double, is (a) 2h (b) 4h (c) 6h (d) 8h 22. A body sliding on a smooth inclined plane requires 4 seconds to reach the bottom starting from rest at the top. How much time does it take to cover one-fourth distance starting from rest at the top (a) 1 s (b) 2 s (c) 4 s (d) 16 s 23. A stone dropped from a building of height h and it reaches after t seconds on earth. From the same building if two stones are thrown (one upwards and other downwards) with the same velocity u and they reach the earth surface after 1 t and 2 t seconds respectively, then (a) 1 2 t = t − t (b) 2 1 2 t t t + = (c) 1 2 t = t t (d) 2 2 2 1 t = t t 24. By which velocity a ball be projected vertically downward so that the distance covered by it in 5th second is twice the distance it covers in its 6th second ( 2 g = 10 m / s ) (a) 58.8 m / s (b) 49 m / s (c) 65 m / s (d) 19.6 m / s 25. Water drops fall at regular intervals from a tap which is 5 m above the ground. The third drop is leaving the tap at the instant the first drop touches the ground. How far above the ground is the second drop at that instant (a) 2.50 m (b) 3.75 m (c) 4.00 m (d) 1.25 m 26. A body is released from a great height and falls freely towards the earth. Another body is released from the same height exactly one second later. The separation between the two bodies, two seconds after the release of the second body is (a) 4.9 m (b) 9.8 m (c) 19.6 m (d) 24.5 m 27. An electron starting from rest has a velocity that increases linearly with the time that is v = kt, where 2 /sec . 2 k = m The distance travelled in the first 3 seconds will be (a) 9 m (b) 16 m (c) 27 m (d) 36 m 28. The acceleration of a particle is increasing linearly with time t as bt. The particle starts from the origin with an initial velocity . 0 v The distance travelled by the particle in time t will be (a) 2 0 3 1 v t + bt (b) 3 0 3 1 v t + bt (c) 3 0 6 1 v t + bt (d) 2 0 2 1 v t + bt 29. The motion of a particle is described by the equation u = at . The distance travelled by the particle in the first 4 seconds (a) 4a (b) 12a (c) 6a (d) 8a 30. A ball is thrown up with a certain velocity so that it reaches a height h. Find the ratio of the times in which it is a h/3. (a) 2 1 2 1 + − (b) 3 2 3 2 + − (c) 3 1 3 1 + − (d) 3 1 31. The displacement of a particle varies with time as x = ae-t + bet where a, , b  are positive constants. The velocity of the particle (a) Will be independent of  and  (b) Drop to zero when  =  (c) Go on decreasing with time (d) Go on increasing with time. 32. The relation between time t and distance x is t = ax2 + bx where a and b are constant. The acceleration is (a) -2abv2 (b) 2bv3 (c) – 2av3 (d) 2av2
33. A particle is moving eastwards with a velocity 5 ms-1 . In 10 s, the velocity changes to 5 ms-1 northwards. The average acceleration in this time is (a) ms NE 2 1 −2 (b) ms N 2 1 −2 (c) Zero (d) ms NW 2 1 −2 34. A parachutist after bailing out falls 50 m without friction. When parachute opens, it decelerates at 2 ms-2 . He reaches the ground with a speed 3 ms-1 . At which height did he bail out? (a) 91 m (b) 182 m (c) 293 m (d) 111 m 35. When a ball is thrown up vertically with a velocity v0 it reaches a height h. If one wishes to triple the maximum height then the ball be thrown with a velocity (a) 3 v0 (b) 3 v0 (c) 9v0 (d) 3/2 v0 36. A car starts from rest, moves with an acceleration a and then decelerates at b for sometime to come to rest. If the total time taken is t, the maximum velocity is (a) abt/a + b (b) a2 t/a + b (c) at/a + b (d) b2 t/a + b 37. Two runners starts simultaneously from the same point one a circular 200 m track in the same direction. Their speeds are 6.2 ms-1 and 5.5 ms-1 . How far from the starting point the faster will overcome the slower? (a) 150 m away from the starting point (b) 170 m away from the starting point (c) 120 m away from the starting point (d) None of these 38. A particle moves according to the equation x = 2t2 – 5t + 6. Find (i) average velocity in the first 3 sec and (ii) velocity at t = 3 s. (a) 1 ms-1 , 7 ms-1 (b) 4 ms-1 , 3 ms-1 (c) 2 ms-1 , 5 ms-1 (d) 3 ms-1 , 7 ms-1 39. A girl after being angry throws here engagement ring from the top of a building 12 m high towards her boy friend with an initial horizontal speed of 5 ms-1 , speed with which the ring it touches the ground is (a) 5 ms-1 (b) 14.3 ms-1 (c) 1.5 ms-1 (d) 16.2 ms- 1 40. The driver of a train A running at 25 ms-1 sights a train B on the same track with 15 ms-1 . The driver of train A applies brakes to produces a deceleration of 1.0 ms-2 . If the trains are 200 m apart, will the trains collide? (a) Yes (b) No` (c) Collision just avoided (d) None of these 41. Two cars A and B are 5 m long each. Car A is at any instant just behind B. A and B are moving at 54 km/h and 36 km/h. Find the road distance covered by the car A to overtake B. (a) 35 m (b) 30 m (c) 32.5 m (d) 27.5 M 42. A particle moves according to the law a = -ky. Find the velocity as a function of distance y, v0 is initial velocity. (a) v2 = v0 2 – ky2 (b) v2 = v0 2 – 2ky (c) v2 = v0 2 – 2ky2 (d) None 43. A particle moves according to the equation dv/dt =  - v where  and  are constants. Find velocity as a function of time. Assume body starts from rest. (a) v = ( ) t 1 e − −   (b) v = ( ) t 1 e − −   (c) t e −   (d) t e −   44. A boat moves relative to water with a velocity v and river is flowering with 2v. At what angle the boat shall move with the stream to have minimum drift? (a) 300 (b) 600 (c) 900 (d) 1200 45. A car starts moving rectilinearly from rest with 5ms-2 form sometime, then uniformly and finally decelerates at 5 ms-2 and come to a stop. The total time of motion equal 25 s. How long does the car move uniformly? Given Vav= 72 km/h during motion. (a) 5s (b) 10 s (c) 15 s (d) 20 s 46. A ship moves along the equator to the east with a speed 30 km/h. Southeastern wind blows 60o to the east with 15 kmh-1 . Find the wind velocity relative to the ship. (a) 39.7 kmh-1 , tan-1 1/5 N of W (b) 23.7 kmh-1 , tan-1 1/3 N of W (c) 37.5 klmh-1 , tan-1 1/5 N of E (b) None of these 47. From a tap 10 m high drops fall at regular intervals. When the first drop reaches the ground, the 5th drop is about to leave the tap. Find the separation between 2nd and 3rd drops. (a) 35/8 m (b) 31/8 m (c) 27/8 m (d) None 48. When a ball is h metre high from a point O, its velocity is v0. When it is hm below O, its velocity is 2v. Find the maximum height from O it will acquire (a) 2h/3 (b) 5h/3 (c) 3h/2 (d) 2h 49. The first stage of the rocket launches a satellite to a height of 50 km and velocity attained is 6000 kmh-1 at which point its fuel exhausted. How high the rocket will reach?
(a) 138.9 km (b) 188.9 km (c) 88.9 km (d) 168.9 km 50. A particle moves according to the equation t = x + 3, when the article comes to rest for the first time (a) 3s (b) 2.5 s (c) 3.5 s (d) None of these 51. A particle of mass m is projected with a velocity j 8 ˆ i 6 ˆ + . Find the change in momentum when it just touches ground. (a) 0 (b) 12 m (c) 16 m (d) 20 m 52. A particle is projected with a velocity j 8 ˆ i 6 ˆ + , 2m away from a vertical wall. After striking the wall it lands at ............... away from the wall. B (a) 3 m (b) 3.3 m (c) 5.5 m (d) 6.6 m 53. A man riding on a flat car moving with 10 ms-1 . He attempts to throw a ball through a stationary hoop 5 m above his hand such that the ball moves horizontally through the hoop. He throws the ball with 12 ms-1 with respect to himself. Find the horizontal distance from where he throws the ball (a) 15 m (b) 14.2 m (c) 16.7 m (d) 18.2 m 54. a body standing on a long railroad car throws a ball straight upwards, the car is moving on the horizontal road with an acceleration 1 ms-2 . The vertical velocity given is 9.8 ms-1 . How far behind the body the ball will fall on the railroad car? (a) 1 m (b) 3/2 m (c) 7/4 m (d) 2 m 55. A person is standing on a truck moving with 14.7 ms-1 on a horizontal road. He throws a ball so that it returns to him when the truck has moved 58.8 m. Find the speed of the ball and angle of projection as seen by a man standing on the road. (a) 22.5 ms-1 , 530 (b) 24.5 ms-1 , 530 (c) 19.6 ms-1 , vertical (d) None of these 56. Six person are situated at the corners of a hexagon of side l. They move at a constant speed v. Each person maintains a direction towards the person at the next corner. When will the person meet? (a) l/v (b) 2l/3v (c) 3l/2v (d) 2l/v. 57. The compass needle of the airplane shows it is heading due North and speedmeter indicates a velocity 240 kmh-1 . Wind is blowing 100 kmh-1 due east. Find the velocity of airplane with respect to earth. (a) 260 ms-1 , 230 E of N (b) 260 ms-1 , 230 W of N (c) 260 ms-1 , 320 E of N (d) None 58. In an exhibition, you win a prize if you toss a coin into a small dish placed. The dish is on a sheep 2.1 m away at a height h from the hand. The coin is tossed into the dish if its velocity is 6.4 ms-1 at an angle of 600 . Find h. (a) 1.2 m (b) 1.35 m (c) 1.5 m (d) 1.65 m 59. A cannon and a target are 5.1 km apart located on the same level. Find the time to hit the target. Speed of cannot is 240 ms- 1 . Assume no air drag. (a) 24.6 s, 42.6 s (b) 24.69s, 48 s (c) 23 s, 46.1s (d) 21s, 41 s 60. A boy can throw a stone to maximum height of 50 m. To what maximum range can he throw this stone and to what height so that the maximum range is maintained? (a) 100 m, 100 m (b) 100 m, 25 m (c) 200 m, 50 m (d) 100 m, 50 m 61. A player throws a ball upwards with an initial speed of 29.4 ms-1 . The height to which the ball rises and the time taken to reach the player's hands are (a) 22.05 m, 38 s (b) 44.1 m, 6s` (c) 29.4 m, 6s (d) 54.5 m, 9s 62. A vehicle moves west with a speed of 50 ms-1 and then towards north with a speed of 50 ms-1 only. Total time taken by the body is 5s. What is the average acceleration of the body? (a) 0 (b) 50ms-2 (c) 14ms-2 (d) 20.4 ms-2 63. A ball is thrown from the ground to clear a wall 3 m high at a distance of 6 m and falls 18 m away from the wall, the angle of projection of ball is (a) tan-1 3/2 (b) tan-1 2/3 (c) tan-1 1/2 (d)tan-1 1/4 64. A wall clock has a 5 cm long minute hand. The average velocity of the tip of the hand reaching 0600 hrs. to 1830 hrs. is (a) 2.2 × 10-14 cms-1 (b) 1.2 × 10 -4 cms-1 (c) 5.6 × 10 -3 cms-1 (d) 3.2 × 10-3 cms-1 65. The acceleration of a particle is increasing linearly with time t as t. If the particle starts from origin with initial velocity u, the distance travelled by it in t second is (a) ut + 1/2 t 3 (b) ut + 1/4 t 3 (c) ut + 1/3 t 3 (d) ut + t 3 /6 66. A drunkard takes a step of 1 m in 1 s. He takes 5 steps forward and 3 steps backward and so on. The time taken by him to fall in a pit 13 m away from the start is (a) 26s (b) 31s (c) 32s (d) 41s 67. A jeep moves at uniform speed of 60 kmh-1 on a straight road blocked by a wall. The jeep has to take a sharp perpendicular turn along the wall. A rocket flying at uniform speed of 100 kmh-1 starts from the wall towards the jeep when the jeep is 30 km away. The rocket reaches the windscreen and returns to wall. Total distance covered by the rocket is