The velocity of a body depends on time according to the equation $v=20+0.1t^2$. The body is undergoing 

1. Uniform acceleration

2. Uniform retardation

3. Non-uniform acceleration

4. Zero acceleration

Which of the following four statements is false?

Two cars \(A\) and \(B\) are travelling in the same direction with velocities \(v_1\) and \(v_2\) \((v_1>v_2).\) When the car \(A\) is at a distance \(d\) behind the car \(B,\) the driver of the car \(A\) applied the brake producing uniform retardation \(a.\) There will be no collision when:
1. \(d < \frac{\left( v_{1} - v_{2} \right)^{2}}{2 a}\)

2. \(d < \frac{v_{1}^{2} - v_{2}^{2}}{2 a}\)

3. \(d > \frac{\left(v_{1} - v_{2}\right)^{2}}{2 a}\)

4. \(d > \frac{v_{1}^{2} - v_{2}^{2}}{2 a}\)

The displacement of a particle is given by $y=a+bt+c{t}^2-d{t}^4$. The initial velocity and acceleration are respectively 

1. $b,-4d$

2. $-b,2c$

3. $b,2c$

4. $2c,-4d$ 

Two trains travelling on the same track are approaching each other with equal speeds of 40 m/s. The drivers of the trains begin to decelerate simultaneously when they are just 2.0 km apart. Assuming the decelerations to be uniform and equal, the value of the deceleration to barely avoid collision should be 

1. 11.8 m/s²

2. 11.0 m/s²

3. 1.6 m/s²

4. 0.8 m/s²

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. $\sqrt{\frac{v}{2a}}$