A man walks on a straight road from his home to a market $2.5\; km$ away with a speed of $5 \;km h ^{-1} .$ Finding the market closed, he instantly turns and walks back home with a speed of $7.5 \;km h ^{-1} .$ What is the average speed of the man over the interval of time $0$ to $40\; min$ ?
A particle moving in a straight line covers half the distance with speed $6 \mathrm{~m} / \mathrm{s}$. The other half is covered in two equal time intervals with speeds 9 $\mathrm{m} / \mathrm{s}$ and $15 \mathrm{~m} / \mathrm{s}$ respectively. The average speed of the particle during the motion is :
Figure gives a speed-time graph of a particle in motion along a constant direction. Three equal intervals of time are shown. In which interval is the average acceleration greatest in magnitude ? In which interval is the average speed greatest ? Choosing the positive direction as the constant direction of motion, give the signs of $v$ and $a$ in the three intervals. What are the accelerations at the points $A, B, C$ and $D$?
A person goes from point $P$ to point $Q$ covering $1 / 3$ of the distance with speed $10 \,km / h$, the next $1 / 3$ of the distance at $20 \,km / h$ and the last $1 / 3$ of the distance at $60 \,km / h$. The average speed of the person is ............ $km / h$
A body is moving with variable acceleration $(a)$ along a straight line. The average acceleration of body in time interval $t_1$ to $t_2$ is