Question
A graph of $v(t)$ is shown for a world-class track sprinter in a 100 -m race. (See Figure 2.79$)$ . (a) What is his average velocity for the first 4 s? (b) What is his instantaneous velocity at $t=5 \mathrm{s} ?(\mathrm{c})$ What is his average acceleration between 0 and 4 $\mathrm{s} ?$ (d) What is his time for the race?
Step 1
From the graph, we can see that the sprinter covers a distance of 12 meters in 4 seconds. Therefore, the average velocity is given by: \[v_{avg} = \frac{d}{t} = \frac{12 m}{4 s} = 6 m/s\] Show more…
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A graph of v(t) is shown for a world-class track sprinter in a 100-m race. (See figure below. For each answer, enter a number.) (a) What is his average velocity (in m/s) for the first 4 s? m/s (b) What is his instantaneous velocity (in m/s) at t = 6 s? m/s (c) What is his average acceleration (in m/s²) between 0 and 4 s? m/s² (d) What is his time (in s) for the race? s
From $t=0$ to $t=5.00 \mathrm{~min},$ a man stands still, and from $t=5.00 \mathrm{~min}$ to $t=10.0 \mathrm{~min},$ he walks briskly in a straight line at a constant speed of $2.20 \mathrm{~m} / \mathrm{s}$. What are (a) his average velocity $v_{\text {arg }}$ and (b) his average acceleration $a_{\mathrm{my}}$ in the time interval $2.00 \mathrm{~min}$ to to 9.00 min? (e) Sketch $x$ versus $f$ and $v$ versus $t,$ and indicate how the answers to (a) through (d) can be obtained from the graphs.
From $t_{0}=0$ to $t_{5}=5.00 \mathrm{~min}$, a man stands still, and from $t_{5}=5.00 \mathrm{~min}$ to $t_{10}=10.0 \mathrm{~min}$, he walks briskly in a straight line at a constant speed of $2.20 \mathrm{~m} / \mathrm{s}$. What are (a) his average velocity $\langle\vec{v}$ ) and (b) his average acceleration $\langle\vec{a})$ in the time interval $2.00 \mathrm{~min}$ to $8.00 \mathrm{~min} ?$ What are (c) $\langle\vec{v}\rangle$ and $\langle\vec{a}\rangle$ in the time interval $3.00 \mathrm{~min}$ to $9.00 \mathrm{~min} ?$ (d) Sketch $x$ vs. $t$ and $v$ vs. $t$, and indicate how the answers to (a) through (c) can be obtained from the graphs.
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