Chapter 2, Problem 50P

(a)

To determine

The instantaneous velocity at $t=10\sec$

Answer to Problem 50P

The instantaneous velocity at $t=10\sec$ is $v=0.28\text{m/s}$

Explanation of Solution

Given:

The given graph is shown below.

  

At $t=10\sec$ rabbit has traveled $3\text{m}$

Formula used:

The instantaneous velocity is calculated as the slope of the tangent line to the curve.

Calculation:

The slope at $t=10\text{s}$ is a line of rise/run. Thus, the instantaneous velocity is

  $\begin{array}{c}v(10)=\frac{\text{14m}}{\text{50s}}\\ =0.28\text{m/s}\end{array}$

Conclusion:

The instantaneous velocity at $t=10\sec$ is $v=0.2\text{8m/s}$

(b)

To determine

The instantaneous velocity at $t=30\sec$

Answer to Problem 50P

The instantaneous velocity at $t=30\sec$ is $v=1.25\text{m/s}$

Explanation of Solution

Given:

The given graph is shown below.

  

The slope line rises to 25 m between $t=17\mathrm{s}\text{to} 37\mathrm{s}$

Calculation:

The instantaneous velocity is

  $\begin{array}{c}v(30)=\frac{25\text{m}-0\text{m}}{37\text{s}-17\text{s}}\\ =1.25\text{m/s}\end{array}$

Conclusion:

The instantaneous velocity at $t=30\sec$ is $v=1.25\text{m/s}$

(c)

To determine

The average velocity between $t=0\sec$ and $t=5\sec$

Answer to Problem 50P

The average velocity of the rabbit between $t=0\sec$ and $t=5\sec$ is $0.3\text{m/s}$

Explanation of Solution

Given:

The given graph is shown below.

  

At $t=5\sec$ is rabbit traveled 1.5 m.

Formula used:

The average velocity is calculated as,

  $\overline{v}=\frac{\Delta s}{\Delta t}$

Calculation:

The average velocity of the rabbit is

  $\overline{v}=\frac{1.5-0}{5-0}=0.30\text{m/s}$

Conclusion:

The average velocity of the rabbit between $t=0\sec$ and $t=5\sec$ is $0.3\text{m/s}$

(d)

To determine

The average velocity between $t=25\sec$ and $t=30\sec$

Answer to Problem 50P

The average velocity of the rabbit between $t=25\sec$ and $t=30\sec$ is $1.6\text{m/s}$

Explanation of Solution

Given:

The given graph is shown below.

  

At $t=25\sec$ , rabbit traveled 8m and at $t=30\sec$ , rabbit travelled 16 m.

Calculation:

The average velocity of the rabbit is

  $\overline{v}=\frac{16\text{m}-8\text{m}}{30\text{s}-25\mathrm{s}}=1.6\text{m/s}$

Conclusion:

The average velocity of the rabbit between $t=25\sec$ and $t=30\sec$ is $1.6\text{m/s}$

(e)

To determine

The average velocity between $t=40\sec$ and $t=50\sec$

Answer to Problem 50P

The average velocity of the rabbit between $t=40\sec$ and $t=50\sec$ is $-1.0\text{m/s}$

Explanation of Solution

Given:

The given graph is shown below.

  

At $t=40\sec$ , rabbit traveled 20 m and at $t=50\sec$ , rabbit travelled 10m

Calculation:

The average velocity of the rabbit is

  $\overline{v}=\frac{10-20}{50-40}=-1.0\text{m/s}$

Conclusion:

The average velocity of the rabbit between $t=40\text{s}$ and $t=50\text{s}$ is $-1.0\text{m/s}$