Two cars \(\mathrm{P}\) and \(\mathrm{Q}\) start from a point at the same time in a straight line and their positions are represented by; \(x_p(t)= at+bt^2\) and \(x_Q(t) = ft-t^2. \) At what time do the cars have the same velocity?

If the velocity of a particle is \(v=At+Bt^{2},\) where \(A\) and \(B\) are constants, then the distance travelled by it between \(1~\text{s}\) and \(2~\text{s}\) is:
1. \(3A+7B\)
2. \(\frac{3}{2}A+\frac{7}{3}B\)
3. \(\frac{A}{2}+\frac{B}{3}\)
4. \(\frac{3A}{2}+4B\)

A particle moves along a straight line OX. At a time t (in seconds), the displacement x (in metres) of the particle from O is given by x= 40 + 12t – t³. How long would the particle travel before coming to rest?

The displacement \(x\) of a particle varies with time \(t\) as \(x = ae^{-\alpha t}+ be^{\beta t}\)$\mathrm{}$
, where \(a,\) \(b,\) \(\alpha,\) and \(\beta\) are positive constants. The velocity of the particle will:

For a particle, displacement time relation is given by $t$ $=$ $\sqrt{x}$ $+$ $3$ . Its displacement, when its velocity is zero will be:
1. \(2\) m
2. \(4\) m
3. \(0\)
4. none of the above