A car starts from rest and travels with uniform acceleration $\alpha$ for some time and then with uniform retardation $\beta$ and comes to rest. If the total travel time of the car is $‘t’$, the maximum velocity attained by it is given by :-
$\frac{\alpha \beta}{(\alpha + \beta)}.t$
$\frac{1}{2} \frac{\alpha \beta}{(\alpha + \beta)}.t^2$
$\frac{\alpha \beta}{(\alpha - \beta)}.t$
$\frac{1}{2} \frac{\alpha \beta}{(\alpha - \beta)}.t^2$
For a particle projected vertically upwards under gravity travels equal distance during $5^{th}$ and $6^{th}$ second of its motion. Find its projection speed........$m/s$ $(g = 9.8\,m/s^2)$
A point moves with uniform acceleration and $\upsilon _1,\upsilon _2$ and $\upsilon _3$ denote the average velocities in the three successive intervals of time $t_1, t_2$ and $t_3$. Which of the following relations is correct
A frictionless wire $AB$ is fixed on a circle of radius $R$. A very small bead slips on this wire. Time taken by bead to slip from $A$ to $B$ is
A person travels along a straight road for half the distance with velocity ${v_1}$ and the remaining half distance with velocity ${v_2}$ The average velocity is given by
Two buses $P$ and $Q$ start from a point at the same time and move in a straight line and their positions are represented by $X _{ P }( t )=\alpha t +\beta t ^{2}$ and $X _{ Q }( t )= ft - t ^{2}$. At what time, both the buses have same velocity $?$