If a car covers $2/5^{th}$ of the total distance with speed $v_1$ and $3/5^{th}$ of the total distance with speed $v_2$,then the average speed is:

$A$ ball is dropped vertically from a height $d$ above the ground. It hits the ground and bounces up vertically to a height $d/2$. Neglecting subsequent motion and air resistance,its velocity $v$ varies with the height $h$ above the ground as:

$A$ point traversed half of the distance with a velocity $v_0$. The remaining part of the distance was covered with velocity $v_1$ for half the time and with velocity $v_2$ for the other half of the time. The mean velocity of the point averaged over the whole time of motion is

For a particle showing motion under the force $F = -5(x - 2)^2$,the motion is .......

$A$ car moves towards north at a speed of $54 \,km/h$ for $1 \,h$. Then it moves eastward with the same speed for the same duration. The average speed and velocity of the car for the complete journey is ..........

$A$ particle of mass $m$ moves on the $x$-axis as follows: it starts from rest at $t = 0$ from the point $x = 0$ and comes to rest at $t = 1$ at the point $x = 1$. No other information is available about its motion at intermediate time $(0 < t < 1)$. If $\alpha$ denotes the instantaneous acceleration of the particle,then