The initial velocity of a particle is u (at t = 0) and the acceleration f is given by at. Which of the following relation is valid 

1. $v=u+a{t}^2$

2. $v=u+a\frac{t^2}{2}$

3. $v=u+at$

4. v = u

The initial velocity of the particle is 10 m/sec and its retardation is 2 m/sec². The distance moved by the particle in 5^th second of its motion is 

1. 1 m

2. 19 m

3. 50 m

4. 75 m

A motor car moving with a uniform speed of 20 m/sec comes to stop on the application of brakes after travelling a distance of 10 m. Its acceleration is 

1. 20 m/sec²

2. –20 m/sec²

3. –40 m/sec²

4. +2 m/sec²

The velocity of a body moving with a uniform acceleration of 2 m/sec² is 10 m/sec. Its velocity after an interval of 4 sec is 

1. 12 m/sec

2. 14 m/sec

3. 16 m/sec

4. 18 m/sec

A particle starting from rest moving with constant acceleration travels a distance x in first 2 seconds and a distance y in next two seconds, then  

1. y = x

2. y = 2x

3. y = 3x

4. y = 4x

The initial velocity of a body moving along a straight line is 7 m/s. It has a uniform acceleration of 4 m/s². The distance covered by the body in the 5^th second of its motion is  

1. 25 m

2. 35 m

3. 50 m

4. 85 m

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?

1. A body can have zero velocity and still be accelerated.

2. A body can have a constant velocity and still have a varying speed.

3. A body can have a constant speed and still have a varying velocity.

4. The direction of the velocity of a body can change when its acceleration is constant.

The position of a particle moving in the XY plane at any time t is given by $x=(3t^2-6t)$ metres. Select the correct statement about the moving particle from the following.

1. The acceleration of the particle is zero at t = 0 second
2. The velocity of the particle is zero at t = 0 second
3. The velocity of the particle is zero at t = 1 second
4. The velocity and acceleration of the particle are never zero