The motion of a particle is described by the equation $x=a+b{t}^2$ where a = 15 cm and b = 3 cm/s². Its instantaneous velocity at time 3 sec will be 

1. 36 cm/sec

2. 18 cm/sec

3. 16 cm/sec

4. 32 cm/sec

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 displacement of a particle, moving in a straight line, is given by $s=2t^2+2t+4$ where s is in metres and t in seconds. The acceleration of the particle is 

1. 2 m/s²

2. 4 m/s²

3. 6 m/s²

4. 8 m/s²

The velocity of a bullet is reduced from 200m/s to 100m/s while travelling through a wooden block of thickness 10cm. The retardation, assuming it to be uniform, will be  

1. $10\times {10}^4$ m/s²

2. $12\times {10}^4$ m/s²

3. $13.5\times {10}^4$ m/s²

4. $15\times {10}^4$ m/s² 

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 \(1\) ms^–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

An object accelerates from rest to a velocity of 27.5 m/s in 10 sec . Then find the distance covered by the object in the next 10 sec:

1. 550 m

2. 137.5 m

3. 412.5 m

4. 275 m

Speed of two identical cars are u and 4u at a specific instant. The ratio of the respective distances in which the two cars are stopped from that instant is:

1. 1 : 1

2. 1 : 4

3. 1 : 8

4. 1 : 16

A car, starting from rest, accelerates at the rate f through a distance S, then continues at a constant speed for time t and then decelerates at the rate $\frac{f}{2}$ to come to rest. If the total distance traversed is 15 S, then, 

1. $S=\frac{1}{2}f{t}^2$

2. $S=\frac{1}{4}f{t}^2$

3. $S=\frac{1}{72}f{t}^2$  

4. $S=\frac{1}{6}f{t}^2$ 

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 120 m long train is moving in a direction with speed 20 m/s. A train B moving with 30 m/s in the opposite direction and 130 m long crosses the first train in a time  

1.  4 s
2.  36 s
3.  38 s
4.  5 s