33. If the velocity of a particle is v = At + Bt2, where A and B are constants, then the distance travelled by it between 1 s and 2 s is:

32. A particle of unit mass undergoes one dimensional motion such that its velocity varies according to v(x) = bx−2n where b and n are constants and x is the position of the particle. The acceleration of the particle as the function of x, is given by:

31. The displacement ’ x ’ (in meter) of a particle of mass ’ m ’ (in kg ) moving in one dimension under the action of a force, is related to time ’ t ’ (in sec) by t = √x+ 3. The displacement of the particle when its velocity is zero, will be

30. A particle has initial velocity ( 2 î + 3 ĵ ) and acceleration ( 0.3 î + 0.2 ĵ ). The magnitude of velocity after 10 seconds will be:

29. The motion of a particle along a straight line is described by equation : x = 8 + 12t − t3 where x is in metre and t in second. The retardation of the particle when its velocity becomes zero, is:

28. A body is moving with velocity 30 m/s towards east. After 10 seconds its velocity becomes 40 m/s towards north. The average acceleration of the body is

27. A particle has initial velocity ( 3 î + 4 ĵ ) and has acceleration ( 0.4 î +0.3 ĵ ). It’s speed after 10 s is:

26. A particle moves a distance x in time t according to equation x = (t + 5)−1. The acceleration of particle is proportional to:

25. A particle starts its motion from rest under the action of a constant force. If the distance covered in first 10 seconds is S1 and that covered in the first 20 seconds is S2, then:

24. The distance travelled by a particle starting from rest and moving with an acceleration 4/3 ms−2 , in the third second is:

23. A particle shows distance-time curve as given in this figure. The maximum instantaneous velocity of the particle is around the point:

22. A particle moves in a straight line with a constant acceleration. It changes its velocity from 10 ms−1 to 20 ms−1 while passing through a distance 135 m in t second. The value of t is:

 

21. The position x of a particle with respect to time t along x-axis is given by x = 9t2 − t3 where x is in metres and t in second. What will be the position of this particle when it achieves maximum speed along the +ve x direction?

20. A particle moving along x-axis has acceleration f, at time t, given by f = f0(1 − t/T) , where f0 and T are constants. The particle at t = 0 has zero velocity. In the time interval between t = 0 and the instant when f = 0, the particle’s velocity (vx) is

19. A particle moves along a straight line OX. At a time t (in seconds) the distance x (in metres) of the particle from O is given by x = 40 + 12t − t3 . How long would the particle travel before coming to rest?

18. The displacement x of a particle varies with time t as x = ae{−αt} +be{βt} , where a, b, α and β are positive constants. The velocity of the particle will

17. The displacement of a particle is represented by the following equation : s = 3t3 + 7t2 + 5t + 8 where s is in metre and t in second. The acceleration of the particle at t = 1 s is

16. A car moving with a speed of 40 km/h can be stopped by applying brakes at least after 2 m. If the same car is moving with a speed of 80 km/h, what is the minimum stopping distance?

15. The displacement of a particle varies with time (t) as: s = at2 − bt3 . The acceleration of the particle will be zero at time t equal to

14. A car accelerates from rest at a constant rate α for some time, after which it decelerates at a constant rate β and comes to rest. If the total time elapsed is t, then the maximum velocity acquired by the car is