Resnick & Halliday Solutions for Chapter: Motion Along a Straight Line, Exercise 1: Problems

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.

The $1992$, the world speed record for a bicycle (human-powered vehicle) was set by Chris Huber. His time through the measured $200 \mathrm{m}$ stretch was a sizzling $6.509 \mathrm{s}$ at which he commented, “Cogito ergo zoom!” (I think, therefore I go fast!). In $2001$, Sam Whittingham beat Huber’s record by $19.0 \mathrm{km} {\mathrm{h}}^{-1}$. What was Whittingham’s time through the $200 \mathrm{m}$?

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.)

In $1 \mathrm{km}$ races runner $1$ on track $1$ (with time $2 \min$, $27.95 \mathrm{s}$) appears to be faster than runner $2$ on track $2$ ($2 \min$, $28.15 \mathrm{s}$). However, the length $L_2$ of track $2$ might be slightly greater than length $L_1$ of track $1$. How large can $L_2-L_1$ be for us still to conclude that runner $1$ is faster?

To set a speed record in a measured (straight-line) distance $d$, a race car must be driven first in one direction (in time $t_1$) and then in the opposite direction (in time $t_2$). 
(a) To eliminate the effects of the wind and obtain the car’s speed $v_{\mathrm{c}}$ in a windless situation should we find the average of $\frac{d}{t_1}$ and $\frac{d}{t_2}$ method  or should we divide $d$ by the average of $t_1$ and $t_2$?

(b)  What is the fractional difference in the two methods when a steady wind blows along the car’s route and the ratio of the wind speed $v_{\mathrm{w}}$ to the car’s speed $v_{\mathrm{c}}$ is $0.0240$?

A pickup vehicle is moving with a speed of $15.00 \mathrm{m} {\mathrm{s}}^{-1}$ on a straight road. A scooterist wishes to overtake the pickup vehicle in $150.0 \mathrm{s}$. If the pickup vehicle is at an initial distance of $1.500 \mathrm{km}$ from the scooterist, with what constant speed should the scooterist chase the pickup vehicle?