The displacement of a particle starting from rest (at t = 0) is given by $s=6t^2-t^3$. The time in seconds at which the particle will attain zero velocity again, is  

1. 2

2. 4

3. 6

4. 8

Two cars A and B are at rest at the same point initially. If A starts with uniform velocity of 40 m/sec and B starts in the same direction with a constant acceleration of 4 m/s², then B will catch A after how much time?

1. 10 sec

2. 20 sec

3. 30 sec

4. 35 sec

The motion of a particle is described by the equation $x=a+b{t}^2$ where a = 15 cm and b = 3 cm/s². Its instantaneous velocity at time 3 sec will be 

1. 36 cm/sec

2. 18 cm/sec

3. 16 cm/sec

4. 32 cm/sec

A body travels for 15 sec starting from rest with constant acceleration. If it travels distances S₁, S₂ and S₃ in the first five seconds, second five seconds and next five seconds respectively the relation between S₁, S₂ and S₃ is 

1. $S_1=S_2=S_3$

2. $5S_1=3S_2=S_3$

3. $S_1=\frac{1}{3}{S}_2=\frac{1}{5}{S}_3$  

4. $S_1=\frac{1}{5}{S}_2=\frac{1}{3}{S}_3$

A body is moving according to the equation $x=at+b{t}^2-c{t}^3$ where x = displacement and a, b and c are constants. The acceleration of the body is 

1. $a+2bt$ 

2. $2b+6ct$ 

3. $2b-6ct$ 

4. $3b-6c{t}^2$ 

A particle travels 10 m in first 5 sec and 10m in the next 3 sec. Assuming constant acceleration what is the distance travelled in next 2 sec ?

1. 8.3 m

2. 9.3 m

3. 10.3 m

4. None of above

The distance travelled by a particle is proportional to the squares of time, then the particle travels with  

1. Uniform acceleration

2. Uniform velocity

3. Increasing acceleration

4. Decreasing velocity

Velocity of a particle changes when 

1. Direction of velocity changes

2. Magnitude of velocity changes

3. Both of above

4. None of the above

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: