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.

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

If body having initial velocity zero is moving with uniform acceleration 8 m/sec² , then the distance travelled by it in fifth second will be  

(1) 36 metres

(2) 40 metres

(3) 100 metres

(4) Zero

An alpha particle enters a hollow tube of 4 m length with an initial speed of 1 km/s. It is accelerated in the tube and comes out of it with a speed of 9 km/s. The time for which it remains inside the tube is

(1) $8\times {10}^{-3} s$

(2) $80\times {10}^{-3}s$

(3) $800\times {10}^{-3}s$

(4) $8\times {10}^{-4}s$

Two cars A and B are travelling in the same direction with velocities v₁ and v₂ $(v_1>v_2)$. When the car A is at a distance d behind car B, the driver of the car A applied the brake producing uniform retardation a. There will be no collision when-

1. $d<\frac{{(v_1-v_2)}^2}{2a}$

2. $d<\frac{v_1^2-v_2^2}{2a}$

3. $d>\frac{{(v_1-v_2)}^2}{2a}$

4. $d>\frac{v_1^2-v_2^2}{2a}$ 

A body of mass 10 kg is moving with a constant velocity of 10 m/s. When a constant force acts for 4 seconds on it, it moves with a velocity 2 m/sec in the opposite direction. The acceleration produced in it is 

(1) 3 m/sec²

(2) –3 m/sec²

(3) 0.3 m/sec²

(4) –0.3 m/sec²