In $25 \min$, a man ran $2.40 \mathrm{km}$ on a treadmill facing east relative to the gym. Find:

(a) the displacement and

(b) the average velocity during this time interval.

Compute your average velocity in the following two cases

(a) You walk $73.2 \mathrm{m}$ at a speed of $1.22 \mathrm{m} {\mathrm{s}}^{-1}$ and run $73.2 \mathrm{m}$ at a speed of $2.85 \mathrm{m} {\mathrm{s}}^{-1}$ along a straight track.

(b) You walk for $1.00$ min at a speed of $1.22 \mathrm{m} {\mathrm{s}}^{-1}$ and then run for $1.00$ min at $3.05 \mathrm{m} {\mathrm{s}}^{-1}$ along a straight track.

(c) Graph $x$ versus $t$ for both the cases and indicate how the average velocity is found on the graph.

A car travels up a hill at a constant speed of $35 \mathrm{km} {\mathrm{h}}^{-1}$ and returns down the hill at a constant speed of $60 \mathrm{km} {\mathrm{h}}^{-1}$. Calculate the average speed for the round trip.

The position of an object moving along an $x‐$axis is given by $x=3t-4t^2+t^3$, where $x$ is in $\mathrm{meters}$ and $t$ in $\mathrm{seconds}$.

Find the position of the object at the following values of $t$,

$\left(a\right) 1 \mathrm{s}$ $\left(b\right) 2 \mathrm{s}$ $\left(c\right) 3 \mathrm{s}$ and $\left(d\right) 4 \mathrm{s}$.

$\left(e\right)$ What is the object’s displacement between $t=0$ and $t=4 \mathrm{s}$?

$\left(f\right)$ What is its average velocity for the time interval from $t=2 \mathrm{s}$ to $t=4 \mathrm{s}$?

$\left(g\right)$ Graph $x$ versus $t$ for $0\le t\le 4 \mathrm{s}$ and indicate how the answer for $\left(f\right)$ can be found on the graph.

A pigeon flies at $36 \mathrm{km} {\mathrm{h}}^{-1}$ to and from between two cars moving towards each other on a straight road, starting from the first car when the car separation is $40 \mathrm{km}$. The first car has a speed of $16 \mathrm{km} {\mathrm{h}}^{-1}$ and the second one has a speed of $25 \mathrm{km} {\mathrm{h}}^{-1}$. By the time the cars meet head-on, what are the

$\left(a\right)$ total distance and

$\left(b\right)$ net displacement is flown by the pigeon?

Panic escape. The figure shows a general situation in which a stream of people attempts to escape through an exit door that turns out to be locked. The people move towards the door at speed $v_{\mathrm{s}}=3.50 \mathrm{m}\mathrm{ }{\mathrm{s}}^{-1}$ are each $d=0.25 \mathrm{m}$ depth and are separated by $L=1.75 \mathrm{m}$. The arrangement in figure occurs at time $t=0$. $\left(a\right)$ At what average rate does the layer of people at the door increase? $\left(b\right)$ At what time does the layer’s depth reach $5.0 \mathrm{m}$? (The answers reveal how quickly such a situation becomes dangerous.)