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

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

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

A body is projected vertically in the upward direction from the surface of the earth. If the upward direction is taken as positive, then the acceleration of the body during its upward and downward journey is:

1. Positive, negative

2. Negative, negative

3. Positive, positive

4. Negative, positive

The velocity v of an object varies with its position x on a straight line as $\mathrm{v}=3\sqrt{\mathrm{x}}$. Its acceleration versus time (a-t) graph is best represented by:

1.		2.
3.		4.