During the first $18\,min$ of a $60\,min$ trip,a car has an average speed of $11\,m/s$. What should be the average speed for the remaining $42\,min$ so that the car has an average speed of $21\,m/s$ for the entire trip (in $,m/s$)?

$A$ 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:

$A$ body is projected vertically up with a velocity $v$ and after some time it returns to the point from which it was projected. The average velocity and average speed of the body for the total time of flight are

When the velocity of a body is variable,then:

$A$ passenger arriving in a new town wishes to go from the station to a hotel located $10 \;km$ away on a straight road from the station. $A$ dishonest cabman takes him along a circuitous path $23 \;km$ long and reaches the hotel in $28 \;min$. What is
$(a)$ the average speed of the taxi,
$(b)$ the magnitude of average velocity? Are the two equal?

$A$ gas balloon is going up with a constant velocity of $10 \text{ m/s}$. When this balloon reached a height of $75 \text{ m}$,a stone is dropped from it and the balloon keeps moving up with the same velocity. The height of the balloon when the stone hits the ground is . . . . . . $\text{m}$. (Take $g = 10 \text{ m/s}^2$)