Question

Austin's truck has a mass of 2000 kg when traveling at 22.0 m/s, it brakes to a stop in 4.0 s. show that the magnitude of the braking force acting on the truck is 11,000 n

Answer 1

Since F=m•a, you want to show that a = -5.5

Answer 2

Since the truck was in motion before the brakes were applied, it will decelerate within the 4s before coming to a stop. Hence the acceleration is $-a\:ms^{-2}$.

When the truck comes to a stop, It will have a final velocity of $v=0\:ms^{-1}$.

Also the initial velocity is 22.0 m/s. This means, $u=22.0\:ms^{-1}$ and time,  $t=4s$.

We can use the relation,

$v=u+at$

to determine the acceleration of the truck.

Let us now plug in all the values to obtain,

$0=22.0+(-a)(4)$

$\Rightarrow -22.0=-4a$

$\Rightarrow \frac{-22.0}{-4}=a$

$\Rightarrow a=5.5 ms^{-2}$

Using the relation,

$F=ma$

the magnitude of the braking force is

$F=2000 \times 5.5 N=11000N$