Question

A car of mass 1100 kg that is traveling at 27 m/s starts to slow down and comes to a complete stop in 578 m. What is the magnitude of the average braking force acting on the car?

Answer 1

A car of mass 1100 kg that is travelling at 27 m/s starts to slow down and comes to a complete stop in 578 m. The magnitude of the average braking force acting on the car is 693 N.

Explanation:

The given car of mass of 1100 kg has been travelling at a speed of 27 m/s and the breaking force was applied. To determine the breaking force, following steps can be undertaken,

Applying the equations of motion, as we know,

                                      $v^{2}=u^{2}-2 a s$

As the car comes to rest, final velocity v=0.  Substituting the known value into the third equation of motion as mentioned above, we get,

                      $0=(27 \times 27)-(2 a \times 578)$

                      $2 a \times 578=27 \times 27$

Then, Deacceleration is

$a=\frac{27 \times 27}{2 \times 578}=\frac{729}{1156}=0.63 \mathrm{m} / \mathrm{s}^{2}$

Now to calculate the force,

                   $F=m a=1100 \times 0.63=693 \mathrm{N}$