Average Velocity and Average Speed

A motorist drives north for $30$ minutes at $85 \mathrm{km}/\mathrm{hr}$ and then stops for $15$ minutes. He continues travelling north and covers $130 \mathrm{km}$ in $2$ hours. What is his total displacement and average velocity?

A car travels the first third of a distance with a speed of $10 \mathrm{km}/\mathrm{hr}$, the second third at $20 \mathrm{km}/\mathrm{hr}$ and last third at$60 \mathrm{km}/\mathrm{hr}$. What is its mean speed over the entire distance? (Answer in $\mathrm{km}/\mathrm{hr}$)

A man walks on a straight road from his home to a market 2.5 km away with a speed of 5 km/h. Finding the market closed, he instantly turns and walks back home with a speed of 7.5 km/h. What is the magnitude of average speed of the man over the time interval 0 to 50 minutes? (Answer in km/h)

A man walks on a straight road from his home to a market $2.5 \mathrm{km}$ away with a speed of $5 \mathrm{km}/\mathrm{h}$. Finding the market closed, he instantly turns and walks back home with a speed of $7.5 \mathrm{km}/\mathrm{h}$. What is the magnitude of average velocity of the man over the time interval $0$ to $50$ minutes? (Answer in $\mathrm{km}/\mathrm{h}$)

A particle moves in a straight line with uniform acceleration. Its velocity at $t=0$ is $v_1$ and at time $t=t$ is $v_2$. The average velocity of the particle in this time travel is $\frac{v_1+v_2}{2}$. Is this correct? Substantiate your answer.

A vehicle travels half of total distance $L$ with speed $v_1$ and the other half with speed $v_2$. What is the average speed?

How is average velocity different from instantaneous velocity?

The velocity-time graph of a particle in one-dimensional motion is shown in Figure.

Which of the following formulae are correct for describing the motion of the particle over the time-interval ${\mathrm{t}}_2$ to ${\mathrm{t}}_1$?

Figure given shows the $x-t$ plot of a particle in one-dimensional motion. Three different equal intervals of time are shown. In which interval is the average speed greatest, and in which is it the least? Give the sign of average velocity for each interval.

A man walks on a straight road from his home to a market $2.5 \mathrm{km}$ away with a speed of $5 \mathrm{k}\mathrm{m} {\mathrm{h}}^{-1}$. Finding the market closed, he instantly turns and walks back home with a speed of $7.5 \mathrm{k}\mathrm{m} {\mathrm{h}}^{-1}$. What is the
(a) magnitude of average velocity, and
(b) average speed of the man over the interval of time (i) $0$ to $30$ min, (ii) $0$ to $50$ min, (iii) $0$ to $40$ min?
[Note: You will appreciate from this exercise why it is better to define average speed as total path length divided by time, and not as the magnitude of average velocity. You would not like to tell the tired man on his return home that his average speed was zero!]

Explain clearly, with examples, the distinction between:
(a) magnitude of displacement (sometimes called distance) over an interval of time, and the total length of path covered by a particle over the same interval;
(b) magnitude of average velocity over an interval of time, and the average speed over the same interval. [Average speed of a particle over an interval of time is defined as the total path length divided by the time interval]. Show in both (a) and (b) that the second quantity is either greater than or equal to the first.
When is the equality sign true? [For simplicity, consider one-dimensional motion only].

A woman starts from her home at $9.00 \mathrm{am}$, walks with a speed of $5 \mathrm{km} {\mathrm{h}}^{-1}$ on a straight road up to her office $2.5 \mathrm{km}$ away, stays at office till $5.00 \mathrm{pm}$, and returns home by an auto with a speed of $25 \mathrm{km} {\mathrm{h}}^{-1}$. Choose suitable scale and plot the $\mathrm{x}-\mathrm{t}$ graph of her motion.