Kinematic Equations for Uniformly Accelerated Motion

Unspecified year 59 questions

1. The graph between displacement and time for a particle moving with uniform acceleration is a/an
2. In a car race on straight road, car A takes a time t less than car B at the finish and passes finishing point with a speed ' v ' more than of car B. Both the cars start from rest and travel with constant acceleration $a_{1}$ and $a_{2}$ respectively. Then ' v ' is equal to:
3. Velocity time curve for a body projected vertically upwards is
4. A bus starts moving with acceleration $2 m/s^{2}$. A cyclist 96 m behind the bus starts simultaneously towards the bus at $20 m/s$. After what time will he be able to overtake the bus?
5. Stopping distance of a moving vehicle is directly proportional to
6. Which of the following graphs gives the equation $x = v_{0}t + \frac{1}{2}a t^{2}$
7. If a train travelling at $20 m/s$ is to be brought to rest in a distance of 200 m, then its retardation should be
8. A body starts from rest and travels ' s ' m in $2^{nd} \text{second}$, then acceleration is
9. A bullet fired into a wooden block loses half of its velocity after penetrating 40 cm. It comes to rest after penetrating a further distance of
10. A body covers 26,28,30,32 meters in $10^{th}$, $11^{th}$, $12^{th}$ and $13^{th} \text{seconds}$ respectively. The body starts
11. The displacement x of a particle at the instant when its velocity is v is given by $v = \sqrt{3x + 16}$. Its acceleration and initial velocity are
12. A particle experiences constant acceleration for 20 seconds after starting from rest. If it travels a distance $s_{1}$ in the first 10 seconds and distance $s_{2}$ in the next 10 seconds, then
13. The distance travelled by a particle starting from rest and moving with an acceleration $4/3 ms^{-2}$, in the third second is:
14. If a car at rest accelerates uniformly to a speed of $144 km/h$ in 20 s, it covers a distance of
15. A car accelerates from rest at a constant rate $\alpha$ for some time, after which it decelerates at a constant rate $\beta$ and comes to rest. If the total time elapsed is t, then the maximum velocity acquired by the car is
16. A bullet is shot vertically downwards with an initial velocity of $100 m/s$ from a certain height. Within 10 s, the bullet reaches the ground and instantaneously comes to rest due to the perfectly inelastic collision. The velocity-time curve for total time $t = 20s$ will be: (Take $g = 10 m/s^{2}$ )
17. A bike accelerates from rest at a constant rate $5 m/s^{2}$ for some time after which it decelerates at a constant rate $3 m/s^{2}$ to come to rest. If the total time elapsed is 8 second, the maximum velocity acquired by the bike is given by
18. A metro train starts from rest and in 5 s achieves $108 km/h$. After that it moves with constant velocity and comes to rest after travelling 45 m with uniform retardation. If total distance travelled is 395 m, find total time of travelling.
19. A car, starting from rest, accelerates at the rate f through a distance S, then continues at constant speed for time t and then decelerates at the rate $f/2$ to come to rest. If the total distance traversed is 15 S, then
20. A particle starting with certain initial velocity and uniform acceleration covers a distance of 12 m in first 3 seconds and a distance of 30 m.in next 3 seconds. The initial velocity of the particle is
21. A body is thrown vertically upwards. If air resistance is to be taken into account, then the time during which the body rises is
22. A body is thrown upwards and reaches half of its maximum height. At that position
23. Velocity-time curve for a body projected vertically upwards is
24. An object accelerated downward under the influence of force of gravity. The motion of object is said to be
25. Free fall of an object (in vacuum) is a case of motion with
26. A ball thrown vertically upwards after reaching a maximum height h, returns to the starting point after a time of 10 s. Its displacement is
27. A ball is released from a height h. If $t_{1}$ and $t_{2}$ be the time required to complete first half and second half of the distance respectively. Then, choose the correct relation between $t_{1}$ and $t_{2}$.
28. The equation represented by the graph below is [add image]
29. A body is projected vertically upwards. If $t_{1}$ and $t_{2}$ be the times at which it is at height h above the projection while ascending and descending respectively, then h is
30. From a tower of height 400 m, a particle is thrown vertically upwards with a speed of $10 m/s$. If the time taken by if to reach the highest point is T then the time taken by the particle to hit the ground is
31. A rocket is fired upward from the earth's surface such that it creates an acceleration of $19.6 ms^{-2}$. If after 5 s, its engine is switched off, the maximum height of the rocket from earth's surface would be
32. A man throws balls with same speed vertically upwards one after the other at an interval of 2sec. What should be the speed of throw so that more than two balls are in air at any time?
33. A ball is dropped from a high rise platform at $t = 0$ starting from rest. After 6 seconds another ball is thrown downwards from the same platform with a speed v. The two balls meet at $t = 18 s$. What is the value of v? (take $g = 10 m/s^{2}$)
34. A stone falls freely under gravity. It covers distances $h_{1}$, $h_{2}$ and $h_{3}$ in the first 5 seconds, the next 5 seconds and the next 5 seconds respectively. The relation between $h_{1}$, $h_{2}$ and $h_{3}$ is
35. From a building two balls A and B are thrown such that A is thrown upwards and B downwards (both vertically). If $T_{A}$ and $T_{B}$ are their respective time of flights then
36. A ball is released from the top of tower of height h metre. It takes T second to reach the ground. What is the position in (m) from the ground of the ball in $T/3 \text{second}$?
37. 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 velocity v varies with the height h above the ground as
38. A stone is dropped into a well in which the level of water is h below the top of the well. If v is velocity of sound, the time T after which the splash is heard is given by
39. A stone is dropped from the top of a building. When it crosses a point 5 m below the top, another stone starts to fall from a point 25 m below the top. Both stones reach the bottom of building simultaneously. The height of the building is
40. The balls are released from the top of a tower of height H at regular interval of time. When first ball reaches at the ground, the $n^{th}$ ball is to be just released and $\left( \frac{n + 1}{2} \right) ^{th}$ ball is at same distance ' h ' from top of the tower. The value of h is
41. A stone is dropped from a rising balloon at a height of 76 m above the ground and reaches the ground in 6 s. What was the velocity of the balloon when the stone was dropped? Take $g = 10 m/s^{2}$.
42. Let A, B, C, D be points on a vertical line such that $AB = BC = CD$. If a body is released from position A, the times of descent through AB, BC and CD are in the ratio.
43. Water drops fall at regular intervals from a tab which is h m above the ground. After how many seconds does the first drop reach the ground?
44. If two balls of masses $m_{1}$ and $m_{2}(m_{1} = 2m_{2})$ are dropped from the same height, then the ratio of the time taken by them to reach the ground will be
45. A boy standing at the top of a tower of 20 m height drops a stone. Assuming $g = 10 ms^{-2}$, the velocity with which it hits the ground is
46. What will be the ratio of the distances moved by a freely falling body from rest on 4th and 5th seconds of journey?
47. A ball released from a height falls 5 m in one second. In 4 seconds it falls through
48. From a balloon moving upwards with a velocity of $12 ms^{-1}$, a packet is released when it is at a height of 65 m from the ground. Time taken by it to reach the ground is $(g = 10 ms^{-2})$
49. A ball dropped from a point A falls down vertically to C, through the midpoint B. The descending time from A to B and that from A to C are in the ratio
50. A ball is dropped from the top of a tower of height 100 m and at the same time another ball is projected vertically upwards from ground with a velocity $25 ms^{-1}$. Then the distance from the top of the tower, at which the two balls meet is
51. A body released from the top of a tower falls through half the height of the tower in 2 s. In what time shall the body fall through the height of the tower?
52. Two bodies of masses $m_{1}$ and $m_{2}$ fall from heights $h_{1}$ and $h_{2}$ respectively. The ratio of their velocities, when they hit the ground is
53. A stone falls from a balloon that is descending at a uniform rate of $12 m/s$. The displacement of the stone from the point of release after 10sec is
54. A body thrown vertically so as to reach its maximum height in t second. Total time from the time of projection to reach a point at half of its maximum height while returning (in sec) is
55. The ratio of distances traversed in successive intervals of time when a body falls freely under gravity from certain height is
56. 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 $(g = 10 m/s^{2})$
57. A stone thrown upward with a speed u from the top of the tower reaches the ground with a velocity 3u. The height of the tower is
58. A stone thrown vertically upwards with a speed of $5 m/\text{sec}$ attains a height $H_{1}$. Another stone thrown upwards from the same point with a speed of $10 m/\text{sec}$ attains a height $H_{2}$. The correct relation between $H_{1}$ and $H_{2}$ is
59. From a pole of height 10 m, a stone is thrown vertically upwards with a speed $5 m/s$. The time taken by the stone, to hit the ground, is n times that taken by it to reach the highest point of its path. The value of n is [take $g = 10 m/s^{2}$]