The motion of a particle is given by the equation $S=(3t^3+7t^2+14t+8)m,$ The value of the acceleration of the particle at t = 1 s is :

The position \(x\) of a particle varies with time \(t\) as \(x=at^2-bt^3\). The acceleration of the particle will be zero at time \(t\) equal to:
1. \(\frac{a}{b}\)
2. \(\frac{2a}{3b}\)
3. \(\frac{a}{3b}\)
4. zero

A body is moving along a straight line according to the equation of motion, x$={\mathrm{t}}^2-3\mathrm{t}+4$, where x is in metre and t is in seconds. What is the acceleration of the body when it comes to rest?

1. Zero

2. $2$ $\mathrm{m}/{\mathrm{s}}^2$

3. $\frac{3}{2}$ $m/s^2$

4. $1$ $\mathrm{m}/{\mathrm{s}}^2$

A particle moves along a straight line such that its displacement at any time t is given by $\mathrm{S}={\mathrm{t}}^3-6{\mathrm{t}}^2+3\mathrm{t}+4$ metres. The velocity when the acceleration is zero is:

The acceleration ‘a’ in m/s² of a particle is given by $a=3t^2+2t+2$ where t is the time. If the particle starts out with a velocity, u = 2 m/s at t = 0, then the velocity at the end of 2 seconds will be:

1. 12 m/s

2. 18 m/s

3. 27 m/s

4. 36 m/s

When the velocity of a body is variable, then:

1. its speed may be constant.

2. its acceleration may be constant.

3. its average acceleration may be constant.

4. All of the above

If the velocity of a particle is given by $v={(180-16x)}^{1/2}$ m/s, then its acceleration will be: 

1. Zero

2. 8 m/s²

3. – 8 m/s²

4. 4 m/s² 

A particle moves a distance x in time t according to equation x = (t+5)^-1. The acceleration of the particle is proportional to: 

If a particle has negative velocity and negative acceleration, its speed: