44. If a ball is thrown vertically upwards with speed u, the distance covered during the last t seconds of its ascent is

43. A man throws balls with the same speed vertically upwards one after the other at an interval of 2 seconds. What should be the speed of the throw so that more than two balls are in the sky at any time? [ Given g = 9.8 m/s2 ]

42. If a ball is thrown vertically upwards with a velocity of 40 m/s, then velocity of the ball after two seconds will be ( g = 10 m/s2 )

41. A body is thrown vertically upward from the ground. It reaches a maximum height of 20 m in 5 sec. After what time, it will reach the ground from its maximum height position?

40. A stone released with zero velocity from the top of a tower, reaches the ground in 4sec. The height of the tower is ( g = 10 m/s2 )

39. Three different objects of masses m1, m2 and m3 are allowed to fall from rest and from the same point O along three different frictionless paths. The speeds of the three objects on reaching the ground will be in the ratio of

38. The water drops fall at regular intervals from a tap 5 m above the ground. The third drop is leaving the tap at an instant when the first drop touches the ground. How far above the ground is the second drop at that instant? ( Take g = 10 m/s2 )

37. 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)

37. 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 (\(g = 10 m/s^2\))

(a) 60 m

(b) 45 m

(c) 80 m

(d) 50 m

Answer :  (b) 45 m

\( s = ut + \)\(\frac{1}{2}\)\(at^2 \)

\( 40 = u_2(2) + \)\(\frac{1}{2}\)\((10)(2)^2 \)

\( 40 = 2u_2 + 20 \)

\(\rightarrow u_2 = 10 \, m/s \)

\( v^2 = u^2 + 2as \)

\( 10^2 = 0 + 2(10)h \)

\( h = 5 \, m \)

total height of the tower = 40 + 5 = 45 m

36. What will be the ratio of the distances moved by a freely falling body from rest in 4th and 5th seconds of journey?

35. A bus is moving with a speed of 10 ms−1 on a straight road. A scooterist wishes to overtake the bus in 100 s. If the bus is at a distance of 1 km from the scooterist, with what speed should the scooterist chase the bus?

34. A train of 150 metre long is going towards north direction at a speed of 10 m/s. A parrot flies at the speed of 5 m/s towards south direction parallel to the railway track. The time taken by the parrot to cross the train is

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: