Chapter 9: Q. 41 (page 229)

A $70$ kg human sprinter can accelerate from rest to $10$ m/s in $3.0$ s. During the same time interval, a $30$ kg greyhound can go from rest to $20$ m/s. What is the average power output of each? Average power over a time interval $∆ t$ is $\frac{∆ E}{∆ t}$

Short Answer

Expert verified

Average power output of sprinter is $1166.67 W$ and of greyhound is $2000 W$ .

Step by step solution

Concept

Concept:
The K.E. of an object moving with velocity is

v

K = \frac{1}{2} m v^{2}

Here

m

is that the mass ofthe thing.
The average output is calculated by dividing the ultimate mechanical energy by the quantity of your time it tookto induce that energy:

P = \frac{K}{ι}

Here

t

is that the time.
Substitute the expression for K.E. within the above equation.

$P = \frac{\frac{1}{2} m v^{2}}{t}$

Typical Power

In the case of the sprinter,the typical power output is:
$P = \frac{\frac{1}{2} m v^{2}}{t}$
Substitute $70 k g$ for mass, $20 m / s$ for speed and $3 s$ for time.

$\begin{aligned} P = \frac{\frac{1}{2} (70 kg) (10 m / s)^{2}}{3 s} \end{aligned}$

$= 1166.67 W$

Step 3. Average power output

The greyhound's average power output is:
$P = \frac{\frac{1}{2} m v^{2}}{t}$

Substitute $30 k g$ for mass, $10 m / s$ for speed, and $3 s$ for time.

\begin{aligned} P = \frac{\frac{1}{2} (30 kg) (20 m / s)^{2}}{3 s} \end{aligned}

$= 2000 W$

So, the greyhound is truly outputting more average power than the sprinter in this period of timel

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A $70$ kg human sprinter can accelerate from rest to $10$ m/s in $3.0$ s. During the same time interval, a $30$ kg greyhound can go from rest to $20$ m/s. What is the average power output of each? Average power over a time interval $∆ t$ is $\frac{∆ E}{∆ t}$

Short Answer

Step by step solution

Concept

Typical Power

Step 3. Average power output

One App. One Place for Learning.

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A 70kg human sprinter can accelerate from rest to 10m/s in 3.0s. During the same time interval, a30 kg greyhound can go from rest to 20 m/s. What is the average power output of each? Average power over a time interval ∆t is ∆E∆t

Short Answer

Step by step solution

Concept

Typical Power

Step 3. Average power output

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Electricity and Magnetism

Physics of Motion

Measurements

Torque and Rotational Motion

Work Energy and Power

Translational Dynamics

Study anywhere. Anytime. Across all devices.

A $70$ kg human sprinter can accelerate from rest to $10$ m/s in $3.0$ s. During the same time interval, a $30$ kg greyhound can go from rest to $20$ m/s. What is the average power output of each? Average power over a time interval $∆ t$ is $\frac{∆ E}{∆ t}$