A ball is thrown vertically into the air and when it returns after an interval of 2 seconds, it is caught. Which one of the following statements is true if the acceleration due to gravity is 10 m/s2 and air resistance can be neglected: (a) The acceleration at the top of its flight is 10 m/s2 (b) The time taken for the descending motion does not equal the time taken for the ascending motion (c) The maximum height it reaches does not depend on the force of gravity (d) The acceleration after it leaves the hand is 10 m/s2 downwardsA ball is thrown vertically up from the top of a building and the graph to the right shows the variation of its velocity with time up to the 5th second. At the end of its journey (as shown by the graph) the ball is: (a) back at its point of projection (b) 25 m from the point of projection and moving downwards (c) 45 m from the point of projection and moving downwards (d) 25 m from the point of projection and moving upwardsWhich of the given velocity-time graphs matches the given acceleration-time graph which you see at the right? (a) (b) (c) (d) A ball is thrown vertically upwards. Ignore air resistance. Take the upward motion as positive. Which one of the following graphs represents the velocity of the ball as a function of time? (a) (b) (c) (d) Two heavy metal spheres P and Q are simultaneously dropped from the same height as shown in the diagram. The sphere P is much smaller than sphere Q. Ignore the effect of air resistance. Which one of the following is the correct observation and possible reason for what happens? (a) Reason: they reach the floor simultaneously Possible reason: gravitational forces are equal for both spheres (b) Reason: they reach the floor simultaneouslyPossible reason: the gravitational acceleration is the same for both (c) Reason: P reaches the floor first Possible reason: smaller objects always fall 'faster' than bigger ones (d) Reason: Q reaches the floor first Possible reason: the earth's force of gravity is greater on the heavier objectAn object is thrown vertically upwards with a speed v from the top of a building. At the same moment, a second object is thrown vertically downwards with the same initial speed v. Which of the following statements regarding the motion of the objects is true (ignore air resistance.)? (a) The object which was thrown upwards reaches the bottom of the building with a higher velocity (b) The object which was thrown downwards reaches the bottom of the building with a higher velocity (c) Both objects reach the bottom with the same velocity at the same time (d) Both objects reach the bottom with the same velocity but at different timesA and B race each other in a 100 metres dash. A wins by 10 metres. They decide to race again, but this time to give B an equal chance, A begins 10 metres behind the start line. Assuming that both run with the same constant speed as before, who is the winner this time? (a) A (b) B (c) Both will finish in the same time (d) Data is inadequateThe velocity-time graph of a moving object is shown in the figure. The acceleration is maximum at point: (a) A (b) B (c) C (d) DWater drops fall at regular intervals from a hole at the bottom of a vessel placed at a high level. The ninth drop is about to fall when the first drop just falls on the floor after being in the air for 2 second. The distance between the 3rd and the 5th drop at this instant is (g = 10 m/s):(a) 39/4 m (b) 25/4 m (c) 6 m (d) 15/4 m10. A ball is thrown upward from the ground. It is at a height of 50 m in upward and downward journeys at times t1 and t2, respectively. If g = 10 m/s2, the t1 t2 is equal to: (a) 5 (b) 10 (c) 15 (d) 2511. Two objects start moving from the same point along the same straight line. The first moves with constant velocity v and the other with constant acceleration a. During the time that elapses before the second catches the first, the greatest distance between them is: (a) (b) (c) (d) 12. A body of mass m, moving along the positive X-direction is subjected to a resistive force F = Kv, where K is a constant and v the particle velocity. If m = 10 kg, v = 10 m/s at t = 0 and K = 2 N/(m/s), the velocity at t = 2 s is: (a) 10/7 m/s (b) – 10/7 m/s (c) 2 m/s (d) 3/7 m/s13. A balloon starts rising from the ground with an acceleration of1.25 m/s2. After 8 s, a stone is released from the balloon. The stone will (g = 10 m/s2): (a) Cover a distance of 40 m in reaching the ground (b) Will have a displacement of 50 m (c) Begin to move down after being released (d) Reach the ground in 4 s14. A ball is thrown vertically upwards. If the air resistance has a constant value: (a) The time of ascent > The time of descent (b) The time of ascent = The time of descent (c) The time of ascent < The time of descent (d) The time of ascent cannot be compared with the time of descent15. 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 balls thrown per minute is (g = 10 m/s2): (a) 40(b) 60 (c) 80(d) 120 16. A body dropped from a height h with an initial speed zero, strikes the ground with a velocity 3 m/s. Another body of same mass is dropped from the same height h with an initial speed of 4 m/s. Find the final velocity of second body, with which it strikes the ground: (a) 3 m/s (b) 4 m/s (c) 5 m/s(d) 12 m/s17. The motion of a body is given by the equation = 6.0 – 3 v(t), where v(t) is speed in m/s and t in sec. If body was at rest at t = 0, which of the following is incorrect: (a) The terminal speed is 2.0 m/s (b) The speed varies with the time as v (t) = 2 (1- e-3t) m/s (c) The speed is 0.1 m/s when the acceleration is half the initial value (d) The magnitude of the initial acceleration is 6.0 m/s218. An elevator ascends upwards with an acceleration of 1.2 m/s2. At the instant its upward speed is 2.5 m/s, a lose bolt drops from the ceiling of the elevator, 3 metre from the floor. What is the time of flight of the bolt from ceiling to the floor? (a) 1.48 sec (b) 0.37 sec (c) 0.74 sec(d) 1.2 sec19. A particle is thrown vertically upward. Its velocity at half of the height is 10m/s, then the maximum height attained by it is (g = 10 m/s2): (a) 8 m (b) 20 m (c) 10 m(d) 16 m20. The position x of a particle varies with time as x = at2 - bt3. The acceleration of the particle is zero at time t which will be equal to: (a) 2a/3b (b) b /a (c) al3b(d) zero21. A body falls freely from rest. It covers as much distance in the last second of its motion as covered in the first three seconds. The body has fallen for a time of: (a) 3 s (b) 5 s (c) 7 s (d) 9 s22. A car travels first half distance between two places with a speed of 30 Km/h and remaining half with a speed of 50 Km/h. The average speed of the car is: (a) 37.5 Km/h (b) 10 Km/h (c) 42 Km/h (d) 40 Km/h23. A particle moving in a straight line with initial velocity u and uniform acceleration f. If the sum of the distances travelled in tth and (t + 1)th seconds is 100 cm, then its velocity after t seconds in cm/s is: (a) 20(b) 30 (c) 50(d) 8024. A rocket is fired upward from the earth's surface such that it creates an acceleration of 19.6 m/sec2. If after 5 sec its engine is switched off, the maximum height of the rocket from earth's surface would be: (a) 245 m(b) 490 m (c) 980 m(d) 735 m25. A ball is dropped on to the floor from a height of 10 m. It rebounds to a height of 2.5 m. If the ball is in contact with the floor for 0.01 seconds, what is the average acceleration during contact? (a) 1400 m/s2 (b) 2100 m/s2 (c) 700 m/s2(d) 2800 m/s226. A ball is thrown up vertically with speed u. At the same instant another ball B is released from rest at height h. At time t, the speed of A relative to B is: (a) u (b) u - 2gt (c) (d) u – gt27. 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 acceleration28. The velocity of a body depends on time according to the equation v = 20 + 0.1 t2. The body is undergoing: (a) uniform acceleration (b) uniform retardation (c) non-uniform acceleration (d) zero acceleration29. A body dropped from top of a tower fall through 40 m during the last two seconds of its fall. The height of tower is (g = 10 m/s2): (a) 60 m(b) 45 m (c) 80m(d) 50m30. A particle moving in a straight line covers half the distance with speed of 3 m/ s. The other half of the distance is covered in two equal time intervals with speed of 4.5 m/s and 7.5 m/s respectively. The average speed of the particle during this motion is: (a) 4.0 m/s (b) 5-0 m/s (c) 5.5 m/s (d) 4.8 m/s31. A balloon is at a height of 81 m and is ascending upwards with a velocity of 12 m/s. A body of 2 kg weight is dropped from it. If g = 10 m/s2, the body will reach the surface of the earth in: (a) 1.5 s (b) 4.025 s (c) 5.4 s(d) 6.75 s32. Two trains travelling on the same track are approaching each other with equal speeds 40 m/sec. The drivers of the trains begin to decelerate simultaneously when they are just 2.0 km apart. Assuming deceleration to be uniform and equal, the value of the deceleration to just avoid the collision should be: (a) 0.8 m/s2 (b) 2.1 m/s2 (c) 11.0 m/s2 (d) 11.8 m/s233. The position of a particle in X-Y plane at any time t is given by x = 3t2 - 6t metre and y = t2 - 2t metre. Select the correct statement: (a) acceleration is zero at t = 0 (b) velocity is zero at t = 0 (c) velocity is zero at t = 1 sec (d) velocity and acceleration of the particle are never zero34. 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) zero35. The deceleration experienced by a moving motor boat, after its engine is cut off, is given by = - kv3 where k is a constant. If Vo is the magnitude of the velocity at cut off, the magnitude of the velocity at time t after the cut off is: (a) Vo (b) Vo/2 (c) Vo e-kt (d) 36. A man in a balloon rising vertically with an acceleration 4.9 m/ sec2 releases a ball 2 second after the balloon is let go from the ground. The greatest height above the ground reached by the ball is: (a) 9.8 m(b) 14.7 m (c) 19.6 m(d) 24.5 m37. A particle moves along a straight line such that the displacements at any time t is given by s = t3 - 6t2 + 3t + 4 metres. The velocity, when the acceleration is zero, is: (a) 3 m/s (b) -9 m/s (c) -12 m/s (d) -6 m/s38. The acceleration of a particle is increasing linearly with time t as bt. The particle starts from the origin with an initial velocity Vo. The distance travelled by the particle in time t will be: (a) Vot + (b) Vot + (c) Vot + (d) Vot + 39. From an elevated point A, a stone is projected vertically upwards. When the stone reaches a distance h below A, its velocity is double of what it was at a height above A. The greatest height attained by the stone is: (a) (b) (c) (d) 40. A target is made of two plates, one of wood and the other of iron. The thickness of the wooden plate is 4 cm and that of iron plate is 2 cm. A bullet fired goes through the wood first and then penetrates 1 cm into iron. A similar bullet fired with the same velocity from opposite direction goes through iron first and then penetrates 2 cm into wood. If a1 and a2 be the retardation offered to the bullet by wood and iron plates respectively then: (a) al = 2a2 (b) a2 = 2a1 (c) a1 = a2 (d) data insufficient41. An object fall from rest. In the last second of its fall it covers half of the total distance. If g = 9.8 m s-2, then the total time of its fall is: (a) 2 + s (b) 2 s (c) 3 + s (d) 5 + s 42. Two balls are projected simultaneously with the same speed from the top of a tower, one vertically upwards and the other vertically downwards. They reach the ground in 9 second and 4 second respectively. The height of the tower is (g = 10 m s-2): (a) 100 m (b) 120 m (c) 180 m (d) 200 m43. A ship travels downstream from point A to point B in two hours and upstream in three hours. Then the time that it will take a log of wood to cover the distance from point A to point B is: (a)12 h (c) 5h (b) 7 h (d) 1 h44. The distance through which a body falls in the nth second is h. The distance through which it falls in the next second is: (a) h (b) h + 2g (c) h – g (d) h + g45. The displacement x of a particle at the instant when its velocity is v is given by v =. Its acceleration and initial velocity are: (a) 1.5 units, 4 units(b) 3 units, 4 units (c) 16 units, 1.6 units(d) 16 units, 3 units46. A particle starts from rest and moves with constant acceleration: Its distance x and velocity v are related as: (a) x v (b) x v2 (c) x v3 (d) x v247. Two bodies begin a free fall from the same height at a time interval of N s. If vertical separation between the two bodies is 1 m after n second from the start of the first body, then n is equal to: (a) (b) (c) + (d) 48. A rocket is fired upward from the earth's surface such that it creates an acceleration of 19.6 m s-2. If after 5 s, its engine is switched off, the maximum height of the rocket from earth's surface would be: (a) 980m (b) 735 m (c) 490 m(d) 245 m49. A particle starts from rest with uniform acceleration a. Its velocity after n second is u. The displacement of the body in the last two second is: (a) (b) (c) (d) 50. A stone is dropped from a certain height which can reach the ground in 5 second. If the stone is stopped after 3 second of its fall and then allowed to fall again, then the time taken by the stone to reach the ground for the remaining distance is: (a) 4 s (b) 3 s (c) 2 s (d) none of these