Two cars \(P\) and \(Q\) 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?
1. \(\frac{a-f}{1+b}\)
2. \(\frac{a+f}{2(b-1)}\)
3. \(\frac{a+f}{2(b+1)}\)
4. \(\frac{f-a}{2(1+b)}\)
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. | \(\frac{3A}{2}+4B\) |
1. | \(24~\text m\) | 2. | \(40~\text m\) |
3. | \(56~\text m\) | 4. | \(16~\text m\) |
The displacement \(x\) of a particle varies with time \(t\) as \(x = ae^{-\alpha t}+ be^{\beta t}\), where \(a,\) \(b,\) \(\alpha,\) and \(\beta\) are positive constants. The velocity of the particle will:
1. | \(\alpha\) and \(\beta.\) | be independent of
2. | go on increasing with time. |
3. | \(\alpha=\beta.\) | drop to zero when
4. | go on decreasing with time. |
For a particle, displacement time relation is given by; . Its displacement, when its velocity is zero will be:
1. \(2\) m
2. \(4\) m
3. \(0\) m
4. none of the above