The motion of a particle is described by the equation u = at, where u is velocity and a is a constant. The distance travelled by the particle in the first 4 seconds 

(1) 4 a

(2) 12 a

(3) 6 a

(4) 8 a

The relation \(3t = \sqrt{3x} + 6\) describes the displacement of a particle in one direction where x is in metres and t in seconds. The displacement, when velocity is zero, is 

The average velocity of a body moving with uniform acceleration travelling a distance of 3.06 m is 0.34 ms^–1. If the change in velocity of the body is 0.18ms^–1 during this time, its uniform acceleration is 

(1) 0.01 ms^–2

(2) 0.02 ms^–2

(3) 0.03 ms^–2

(4) 0.04 ms^–2

Equation of displacement for any particle is $s=3t^3+7t^2+14t+8m$. Its acceleration at time t = 1 sec is 

1. 10 m/s²

2. 16 m/s²

3. 25 m/s²

4. 32 m/s²  

The position of a particle moving along the x-axis at certain times is given below :

Which of the following describes the motion correctly?  

(1) Uniform, accelerated

(2) Uniform, decelerated

(3) Non-uniform, accelerated

(4) There is not enough data for generalization

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 displacement of a particle, moving in a straight line, is given by $s=2t^2+2t+4$ where s is in metres and t in seconds. The acceleration of the particle is 

(1) 2 m/s²

(2) 4 m/s²

(3) 6 m/s²

(4) 8 m/s²

A body A starts from rest with an acceleration a₁. After 2 seconds, another body B starts from rest with an acceleration a₂. If they travel equal distances in the 5th second, after the start of A, then the ratio a₁: a₂  is equal to:

(1) 5: 9

(2) 5: 7

(3) 9: 5

(4) 9: 7

The velocity of a bullet is reduced from 200m/s to 100m/s while travelling through a wooden block of thickness 10cm. The retardation, assuming it to be uniform, will be  

(1) $10\times {10}^4$ m/s²

(2) $12\times {10}^4$ m/s²

(3) $13.5\times {10}^4$ m/s²

(4) $15\times {10}^4$ m/s² 

A particle starts from rest, accelerates at 2 m/s² for 10s and then goes for constant speed for 30s and then decelerates at 4 m/s² till it stops. What is the distance travelled by it?

(1) 750 m

(2) 800 m

(3) 700 m

(4) 850 m