Chapter 9: Q. 40 (page 229)

A $50$ kg sprinter, starting from rest, runs $50$ m in $7.0$ s at constant acceleration.
a. What is the magnitude of the horizontal force acting on the sprinter?
b. What is the sprinter’s power output at $2.0$ s, $4.0$ s, and $6.0$ s?

Short Answer

Expert verified

a). Horizontal force is 102.04 N

b). Out power at t=2 s is 416.32 W, at t=4 s is 832.64 W and at t=6 s is 1284.96 W

Step by step solution

Step 1. Given Information

We have,

Mass $m = 50$ kg

$s = 50$ m in $7.0$ s at constant acceleration

Step 2. Find the acceleration

Magnitude of force can be found second Newton's law $F = m a$

Acceleration of sprinter can be found form equation from kinematics that connects distance, time and constant acceleration

$s = \frac{1}{2} a t^{2} \Rightarrow a = \frac{2 s}{t^{2}} a = \frac{2 \cdot 50 m}{{(7 s)}^{2}} a = 2.04 m / s^{2}$

Step 3. Part a). Find the magnitude of force

So,

$F = m a F = 50 k g \cdot 2.04 m / s^{2} F = 102.04 N$

Part b). Find the sprinter output power

Output power can be found from $P = F v$

$P_{t = 2 s} = 102.04 N \cdot 2.04 m / s^{2} \cdot 2 s = 416.32 W P_{t = 4 s} = 102.04 N \cdot 2.04 m / s^{2} \cdot 6 s = 832.64 W P_{t = 6 s} = 102.04 N \cdot 2.04 m / s^{2} \cdot 6 s = 1248.96 W$

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A $50$ kg sprinter, starting from rest, runs $50$ m in $7.0$ s at constant acceleration.
a. What is the magnitude of the horizontal force acting on the sprinter?
b. What is the sprinter’s power output at $2.0$ s, $4.0$ s, and $6.0$ s?

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Find the acceleration

Step 3. Part a). Find the magnitude of force

Part b). Find the sprinter output power

One App. One Place for Learning.

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A 50kg sprinter, starting from rest, runs 50m in 7.0s at constant acceleration. a. What is the magnitude of the horizontal force acting on the sprinter?b. What is the sprinter’s power output at 2.0s, 4.0s, and6.0 s?

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Find the acceleration

Step 3. Part a). Find the magnitude of force

Part b). Find the sprinter output power

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Turning Points in Physics

Circular Motion and Gravitation

Wave Optics

Magnetism

Solid State Physics

Work Energy and Power

Study anywhere. Anytime. Across all devices.

A $50$ kg sprinter, starting from rest, runs $50$ m in $7.0$ s at constant acceleration.
a. What is the magnitude of the horizontal force acting on the sprinter?
b. What is the sprinter’s power output at $2.0$ s, $4.0$ s, and $6.0$ s?