The displacement of a particle starting from rest (at t = 0) is given by $s=6t^2-t^3$. The time in seconds at which the particle will attain zero velocity again, is  

(1) 2

(2) 4

(3) 6

(4) 8

Consider the acceleration, velocity and displacement of a tennis ball as it falls to the ground and bounces back. Directions of which of these changes in the process ?

1. Velocity only

2. Displacement and velocity

3. Acceleration, velocity and displacement

4. Displacement and acceleration

The engine of a motorcycle can produce a maximum acceleration 5 m/s². Its brakes can produce a maximum retardation 10 m/s². What is the minimum time in which it can cover a distance of 1.5 km?

(1) 30 sec

(2) 15 sec

(3) 10 sec

(4) 5 sec

A student is standing at a distance of 50 metres from the bus. As soon as the bus begins its motion with an acceleration of 1ms^–2, the student starts running towards the bus with a uniform velocity u. Assuming the motion to be along a straight road, the minimum value of u, so that the student is able to catch the bus is 

1. 5 ms^–1

2. 8 ms^–1

3. 10 ms^–1

4. 12 ms^–1

A body A moves with a uniform acceleration a and zero initial velocity. Another body B, starts from the same point moves in the same direction with a constant velocity v. The two bodies meet after a time t. The value of t is 

1. $\frac{2v}{a}$

2. $\frac{v}{a}$

3. $\frac{v}{2a}$

4. $\sqrt{\frac{v}{2a}}$ 

A particle moves along X-axis in such a way that its coordinate X varies with time t according to the equation $x=(2-5t+6t^2)m$. The initial velocity of the particle is 

(1) –5 m/s

(2) 6 m/s

(3) –3 m/s

(4) 3 m/s 

A man is 45 m behind the bus when the bus starts accelerating from rest with acceleration of 2.5 m/s². With what minimum velocity should the man start running to catch the bus? 

1. 12 m/s

2. 14 m/s

3. 15 m/s

4. 16 m/s

A ball is dropped on the floor from a height of 10 m. It rebounds to a height of 2.5 m. If the ball is in contact with the floor for 0.01 sec, the average acceleration during contact is 

(1) 2100 m/sec² downwards

(2) 2100 m/sec² upwards

(3) 1400 m/sec²

(4) 700 m/sec²

A ball of mass m₁ and another ball of mass m₂ are dropped from equal height. If time taken by the balls are t₁ and t₂ respectively, then 

1. $t_1=\frac{t_2}{2}$

2. $t_1=t_2$

3. $t_1=4t_2$

4. $t_1=\frac{t_2}{4}$ 

Velocity of a body on reaching the point from which it was projected upwards, is 

1. $v=0$

2. $v=2u$

3. $v=0.5u$

4. $v=-u$