Question on equations of motion
1. A car has initial velocity of 72 km h^-1. It is accelerated at 2 m s ^- 2 Calculate the final velocity and the distance covered after 3 seconds.
[Ans. 26 m s ^-1, 69 m]
2. A body is moving with uniform acceleration of 10 m s^-2. If it starts from rest, calculate its displacement after 5 s.
[Ans. 125 m]
3. A car at rest accelerates uniformly to a speed of 144 km h^-1 in 20s. How much distance is covered by the car ?
[Ans. 400 m]
4. Brakes are applied to a car travelling at 30 m s ^- 1 . Its velocity is reduced to 20 m s ^- 1 in 5 seconds. Calculate the retardation produced by the brakes. Also calculate the distance covered in those 5 seconds.
[Ans. 2 m s ^- 2, 125 m]
5. A body starts from rest and acquires a velocity of 12 m s ^-1 in 5 s. Calculate the acceleration and distance moved.
[Ans. 2.4 m s ^ – 2, 30 m ]
6. A car is moving velocity of 72 km h ^ – 1 Its velocity is reduced to 36 km h ^ – 1 after covering a distance of 200 m. Calculate retardation in cm s ^- 2
[Ans. 75 cm s^-2 ]
7. Starting from rest, an aeroplane takes off after covering 0.7 km on the runway. If it takes off at 35m s ^- 1 calculate (a) the acceleration (b) time for which it on the runway.
[Ans. (a) 0.875 s ^-2 (b) 40 s]
8. An automobile travelling with a speed of 60 h ^- 1 can brake to stop within a distance of 20 m. If the car is going twice as fast i. e 120 km /h, find the stopping distance.
[Ans. 80 m ]
9. A body moving with a uniform acceleration travels distances of 24 m and 64 m during the first two equal consecutive intervals of time, each of duration 4 s. Determine the initial velocity and acceleration of the moving body.
[Ans. 1 m/s : 2.5 m s^-2 ]
10. A body travels a distance of 2 min 2 s and 2.8 m in next 4 s. What will be speed of the body at the end of 10th second from the start.
[Ans. 0.1 m s ^-1 ]
11. A body leaving a certain point O moves with an acceleration, which is constant in magnitude and direction. At the end of the fifth second, its velocity is 1.5 m s ^- 1. At the end of the sixth second, the body stops and then begins to move backwards.
(a) Find the distance traversed by the body, before it stops.
(b) Determine the velocity with which the body returns to point O.
[Ans. (a) 27 m (b) 9 m s ^- 1 ]
12. A hundred metre sprinter increases her speed from rest uniformly at the rate of 1.5 m s^-2 up to three quarters of the total run and covers the last quarter with uniform speed. How much time does she take to cover the first half and the second half of the run ?
[Ans. 8.165 s, 3-502 s]
13. A stone is thrown vertically upwards with an initial velocity of 14m s ^- 1 Find the maximum height reached and the time of ascent. Given s = 9.8m s ^- 2
[Ans. 10 m, 1.429 s]
14. A balloon is moving upwards with a speed of 5m s ^- 1 When it is at a height of 98 m, a packet is dropped from it. What is the velocity of the packet, when it strikes the ground ?
[Ans. 44.1 m s ^- 1 ]
15. From the top of a tower 100 m in height, a ball is dropped and at the same time another ball is projected vertically upwards from the ground with a velocity of 25 m s^- 1. Find when and where the two balls will meet? (g = 9.8 m s ^- 2)
[Ans. 4 s, 78.4 m (from the top)]
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