graphical problems in motion

Graphs of motion by VKS Tewari 1. A tennis ball is released so that it falls vertically to the floor and bounces again. Taking velocity upwards as positive, which of the following graphs best represents the variation of its velocity u with time t ? 2. A body moves from rest with a constant acceleration. Which one of the following graphs represents the variation of its kinetic energy Ek with the distance S traveled? 3. The displacement of a particle as a function of time is shown in Fig. The figure indicates that (a) The particle starts with a certain velocity but the motion is retarded and finally the particle stops (b) The velocity of the particle is constt. throughout (c) The acceleration of the particle is constant (d) The particle starts with a constant velocity, the motion is accelerated and finally the particle moves with another constant velocity 10 20 s in m ® 10 20 30 40 50 t in sec. ® ­ Ek S ® (a) ­ Ek S ® (b) ­ Ek S ® (c) ­ Ek S ® (d) + – v0 t (a) + – v0 t (b) + – v0 t (c) + – v0 t (d) Graphs of motion by VKS Tewari 4. The graph between the displacement x and time t for a particle moving in a straight line is shown in the diagram. During the intervals OA, AB, BC and CD the acceleration of the particle is : OA AB BC CD (a) + 0 + + (b) – 0 + 0 (c) + 0 – + (d) – 0 – 0 5. Figure shows some velocity versus time graphs : Only some of these can be realized in particle. These are: (a) (A), (B) and (D) (b) (A), (B) and (C) (c) (B), (D) (d) All 6. Which of the following figures represents the motion of a body moving in a straight line under constant acceleration ? ­ v (a) ­ v t ® (b) (c) ­ v (d) t ® t ® ­ v t ® Velocity ® Time ® (A) (B) (C) (D) Time ® Velocity ® Time ® Velocity ® Velocity ® Time ® s O t A B C D Graphs of motion by VKS Tewari 7. A particle is thrown vertically upwards with a velocity u. It returns to the ground in time T. Which of the following graphs correctly represents the motion ? 8. Velocity versus time graph of a body is shown in Fig. It explain that : (a) At B force is zero (b) At B there is a force but towards motion (c) At B there is a force but opposes the motion (d) Force are equal at A, B and C 9. The velocity versus time curve of a moving point is shown in Fig. the retardation is : (a) 1 cm/sec2 (b) 2 cm/sec2 (c) 3 cm/sec2 (d) 4 cm/sec2 10. The area of the shaded portion of the graph represents : (a) The average acceleration (b) The maximum KE (c) The momentum (d) The displacement ­ v t ® 0 10 20 50 40 30 60 70 20 40 60 ­ v t ® A B C t ® ­ v Velocity (a) v (b) (c) v (d) T/2 Time ® V T O T V T/2 –v T/2 Time ® –v O T/2 T Graphs of motion by VKS Tewari 11. The velocity versus time graph of a body moving in a straight line is as follows. The distance traveled by the body in 5 sec is (a) 2 m (b) 3 m (c) 4 m (d) 5 m 12. The velocity versus time graph of a linear motion is shown in the Fig. The distance form the origin after 8 sec is : (a) 18 m (b) 16 m (c) 8 m (d) 6 m 13. An object is dropped from rest. Its velocity versus displacement graph is : 14. Which of the following position-time graph does not exist in nature ? (a) (b) (c) (d) ­ x t ® t ® ­ x ­ x t ® t ® 1 2 3 4 5 6 7 8 t in sec. –2 0 2 4 1.5 1 2 3 5 t in sec. v in m/sec. ® –2 –1 0 +1 +2 v in m/sec. ® ­ v S ® (a) ­ v S ® (b) ­ v S ® (c) ­ v S ® (d) Graphs of motion by VKS Tewari 15. In the two dimensional motions (a) x-t graph gives actual path of the particle (b) y-t graph gives actual path of the particle (c) versus t graph gives the actual path of the particle (d) y-x graph gives actual path of particle 16. In the given x-t curve, 17. A particle move along X-axis whose velocity varies with time as shown in the figure. Then which of the following graph is/are correct (d) all the above 18. The position of a particle at any instant t is given by x = a cos wt. The speed-time graph of the particle is 2 2 y x + Time ® Speed (a) Displacement (b) Time ® Acceleration (c) Time ® t® A B C D v A B C ­ x t® x (a) the velocity at A is zero but at B is non-zero (b) the velocity at A and B is zero (c) the velocity at A and B non-zero (d) the directions of velocity at A and B are definite t® v (a) t® v (b) t® v (d) t® v (c) Graphs of motion by VKS Tewari 19. The acceleration of a train between two stations 2 km apart is shown in the figure. The maximum speed of the train is (a) 60 m/s (b) 30 m/s (c) 120 m/s (d) 90 m/s 20. The velocity-time plot for a particle moving on a straight line is shown in the figure, then (a) the particle has a constant acceleration (b) the particle has never turned around (c) the average speed in the interval 0 to 10 s is the same as the average speed in the interval 10 s to (d) both (a) and (c) are correct 21. A ball is dropped vertically from a height d above the ground. It hits the ground and bounces up vertically to a height d/2. neglecting subsequent motion and air resistance, its speed u varies with the height h above the ground as 4 8 12 16 –5– +5– m/s2® t(s)® 10 20 30 11V(m/s) t(s)® (a) (b) (c) (d) Graphs of motion by VKS Tewari 22. A ball is projected vertically upwards. If resistance due to air is ignored, then which of the following graphs represent the velocity time graph of the ball during its flight? 23. An object is thrown upward with a velocity u, then displacement-time graph is 24. Two stone A and B are dropped from a multistoried building with a time interval t0, where t0 smaller than the time taken by A to reach the floor. At t = t0, stone A is dropped. After striking the floor, stone comes to rest. The separation between stones plotted against the time lapse t is best represented by (a) (b) (c) (d) t® (a) (b) 2g u2 ­ s t® 2g u2 ­ s t® (c) (d) ­ s t® ­ s t® (a) (b) (c) (d) t® d d t0 t® t® t® d d Graphs of motion by VKS Tewari 25. A stone is released from a balloon moving upward with velocity u0 at height h at t = 0. Which of the following graph is best representation of velocity-time graph for the motion of stone? 26. The displacement time graph is show in figure. The instantaneous velocity is negative at the point (a) D (b) F (c) C (d) E 27. A balloon going upward with a velocity of 12 m/s is at a height of 65m from the earth surface at any instant. Exactly at this instant a packet drops from it. How much time will the packet take in reaching the surface of earth? (g = 10m/s2) (a) 7.5 sec (b) 10 sec (c) 5 sec (d) none of these 28. In the previous problem draw speed-time graph. (b) (b) (a) v t® v t® v t® (d) none of these (a) (b) (c) (d) t® v t® v t® v t® v C D E F Displacement ® Time ® Graphs of motion by VKS Tewari 29. If co-ordinates of a moving point at time t are given by x = a (t + sin t), and y = a (1– cos t), then (a) the slope of acceleration time graph is zero (b) the slope of velocity-time graph is constant (c) the direction of motion makes an angle t/2 with x-axis (d) all the above 30. Which of the following graphs represents motion with uniform velocity? 31. The displacement time graph for two particles A and B are straight lines inclined at angles of 30o and 60o with the time axis. The ratio of the speed uA : uB is : (a) 1 : 2 (b) 3 : 1 (c) 1 : 3 (d) 1 : 3 32. A rocket is fired upwards. Its velocity versus time graph is shown in Fig. The maximum height reached by the rocket is : 33. In the above problem the acceleration of the rocket during burning interval is : (a) (1200/12) m/s2 (b) (12/1200) m/s2 (c) (1200 × 12) m/s2 (d) (1200/132) m/s2 20 40 60 80 100 120 132 12 t in sec ® 140 1200 600 V in m/sec. ® ­ s t ® (a) ­ s t ® (b) ­ a t ® (c) ­ a t ® (d) (a) 7.1 km (b) 79.2 km (c) 72 km (d) Infinite Graphs of motion by VKS Tewari 34. Two stone A and B are dropped from a multistoried building with time interval t, where t0 smaller than the time taken by A to reach the floor. At t = t0, stone A is dropped. After striking the floor, stone comes to rest. The separation between stones plotted against the time lapse t is best represented by 35. Velocity-displacement graph of a particle moving in a straight line is as shown in figure. v s (a) (b) (c) (d) t® d d t0 t® t® t® d d a. magnitude of acceleration of particle is decreasing b. magnitude of acceleration of particle is increasing c. acceleration versus displacement graph is straight line d. acceleration versus displacement graph is parabola