A point moves with uniform acceleration and v₁, v₂ and v₃ denote the average velocities in the three successive intervals of time t₁, t₂ and t₃. Which of the following relations is correct ?

(1) $(v_1-v_2):(v_2-v_3)=(t_1-t_2):(t_2+t_3)$

(2) $(v_1-v_2):(v_2-v_3)=(t_1+t_2):(t_2+t_3)$

(3) $(v_1-v_2):(v_2-v_3)=(t_1-t_2):(t_1-t_3)$

(4) $(v_1-v_2):(v_2-v_3)=(t_1-t_2):(t_2-t_3)$ 

The acceleration of a moving body can be found from: 

(1) Area under the velocity-time graph

(2) Area under the distance-time graph

(3) Slope of the velocity-time graph

(4) Slope of the distance-time graph

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

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.

A particle moving with a uniform acceleration travels 24 m and 64 m in the first two consecutive intervals of 4 sec each. Its initial velocity is 

(1) 1 m/sec

(2) 10 m/sec

(3) 5 m/sec

(4) 2 m/sec

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