Answer:
28,699m
Explanation:
The force to make the box move should be μs.N=μs.m.g=m.|a|
then,
|a|=μs.g
Being
μs coefficient of static friction,
N the force made by the truck on the box caused by the gravity force,
m the mass,
g the acceleration of gravity
and a the acceleration of the truck.
[tex]x = v \times t + \frac{1}{2} \times a \times {t}^{2} [/tex]
as the truck is stopping, the acceleration is negative. then,
[tex]x = v \times t - \frac{1}{2} \times |a| \times {t}^{2} [/tex]
[tex] |a| = v \div t \\ t = v \div |a| [/tex]
[tex]x = v \times (v \div |a| ) - \frac{1}{2} \times |a| \times {(v \div |a|)}^{2} [/tex]
[tex]x = v \times (v \div μs.g ) - \frac{1}{2} \times |a| \times {(v \div μs.g)}^{2} [/tex]
[tex]x = \frac{{v}^{2}}{μs \times g} - \frac{1}{2} \times \frac{{v}^{2}}{μs \times g} \\ x = \frac{1}{2} \times \frac{{v}^{2}}{μs \times g} \\ x = 0.5 \times \frac{{(15m/s) }^{2} }{0.4 \times 9.8m/ {s}^{2} } = 28.699m[/tex]
28,699m
