Chapter 3, Problem 6TS

Leroy, who has a mass of is skateboarding at when he smacks into a brick wall and comes to a dead stop in .

(a) Show that his deceleration is .

(b) Show that the force of impact is . (ouch!)

To determine

The deceleration is 45 m/s².

Answer to Problem 6TS

The deceleration is, 45 m/s².

Explanation of Solution

Given info: The initial speed of the skateboard is 0.9 m/s, the final speed of the skateboard is 0 m/s and the time taken is 0.2 s.

Write the expression for the deceleration.

$a=\frac{v-u}{t}$

Here,

v is the initial velocity

u is the final velocity

t is corresponding time

Substitute 9.0 m/s for v, 0 for u and 0.2 s for t in the above equation to get a.

$\begin{array}{l}a=\frac{9\text{m}/\text{s}-0}{0.2\text{s}}\\ a=45{\text{m}/\text{s}}^2\end{array}$

Conclusion:

Therefore, the deceleration is 45 m/s² .

To determine

The force of impact is 4500 N.

Answer to Problem 6TS

The force of impact is 4500 N.

Explanation of Solution

Given info: The initial speed of the skateboard is 0.9 m/s, the final speed of the skateboard is 0 m/s and the time taken is 0.2 s.

Write the expression for the force exerted.

$F=ma$

Here,

m is the mass

a is the acceleration

Substitute 100 kg for m, and 45m/s² for a in the above equation to get F.

$$\begin{array}{l}F=100\text{kg}\times 45\text{m}/{\text{s}}^{\text{2}}\\ F=4500\text{N}\end{array}$$

Conclusion:

Therefore, the force of impact is 4500 N.