The positions of two cars $A$ and $B$ are $X_A = at + bt^2,$ $X_B = ft -t^2$ At what time Both cars will have same velocity

- A
$\frac{a+f}{2(1+b)}$

- B
$\frac{f-a}{2(1+b)}$

- C
$\frac{a-f}{1+b}$

- D
$\frac{a+f}{2(b-1)}$

A particle is projected with velocity $v_0$ along $x-$ axis and its decelaration on the particle is a $a= -\alpha x^2$. The distance at which the particle stops is

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

The displacement-time graph for two particles $A$ and $B$ are straight lines inclined at angles of $30^o$ and $60^o$ with the time axis. The ratio of velocities of $V_A : V_B$ is

A man is, $d$ distance behind a bus. The bus moves away from the man with an acceleration $a$. At the same time, man starts running towards bus with a constant velocity $v$.

Let $v$ and $a$ denote the velocity and acceleration respectively of a body