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Q2.5-33PE

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Found in: Page 35

### College Physics (Urone)

Book edition 1st Edition
Author(s) Paul Peter Urone
Pages 1272 pages
ISBN 9781938168000

# An unwary football player collides with a padded goalpost while running at a velocity of 7.50 m/s and comes to a full stop after compressing the padding and his body 0.350. (a) What is his deceleration? (b) How long does the collision last?

a) -80.36 m/s2

b) 0.0933 s

See the step by step solution

## Given Data

• The initial velocity of the football, U = 7.50 m/s.
• The final velocity of the football, V = 0 m/s.
• The distance traveled in compressing the padding, D = 0.350 m.

## Deceleration and time period

a) The deceleration of the football can be calculated using the equation as:

${V}^{2}-{U}^{2}=2ad$ Here V is the final velocity, U is the initial velocity, a is the acceleration, and d is the distance traveled.

Substituting values in the above expression, we get,

$\left(0{\right)}^{2}-\left(7.5{\right)}^{2}=2×\left(0.35\right)×a\phantom{\rule{0ex}{0ex}}-56.25=2×\left(0.35\right)×a\phantom{\rule{0ex}{0ex}}a=\frac{-56.25}{2×\left(0.35\right)}\phantom{\rule{0ex}{0ex}}a=-80.357{\text{m/s}}^{\text{2}}$

The deceleration of the football is -80.357 m/s2.

b) The time required can be calculated as:

V = U + at

Here V is the final velocity, U is the initial velocity, a is the acceleration, and t is the time.

Substituting values in the above expression, we get,

$0=7.5+\left(-80.36\right)×t\phantom{\rule{0ex}{0ex}}t=\frac{7.5}{80.36}\phantom{\rule{0ex}{0ex}}t=0.0933\text{s}$

Hence the time period is 0.0933 s.