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

A body starts from rest from the origin with an acceleration of $6m/s^2$ along the x-axis and $8m/s^2$ along the y-axis. Its distance from the origin after 4 seconds will be 

(1) 56 m

(2) 64 m

(3) 80 m

(4) 128 m

A car moving with a velocity of 10 m/s can be stopped by the application of a constant force F in a distance of 20 m. If the velocity of the car is 30 m/s, it can be stopped by this force in 

(1) $\frac{20}{3}m$

(2) 20 m

(3) 60 m

(4) 180 m

The displacement of a particle is given by $\mathrm{y}=\mathrm{a}+\mathrm{bt}+{\mathrm{ct}}^2-{\mathrm{dt}}^4$. The initial velocity and acceleration are, respectively: