Question

A 2498 kg car is moving at 17.1 m/s slams on its brakes and slows to 2.6 m/s. What is the magnitude (absolute value) of the impulse the car experiences during this time?

Answer 1

J=36221 Kg.m/s

Step-by-step explanation:

Impulse-Momentum Theorem

These two magnitudes are related in the following way. Suppose an object is moving at a certain speed
`v_1` and changes it to
`v_2`. The impulse is numerically equivalent to the change of linear momentum. Let's recall the momentum is given by

`p=mv`

The initial and final momentums are, respectively

`p_1=mv_1,\ p_2=mv_2`

The change of momentum is

`\Delta p=p_2-p_1=m(v_2-v_1)`

It is numerically equal to the Impulse J

`J=\Delta p`

`J=m(v_2-v_1)`

We are given

`m=2498\ kg,\ v_1=17.1\ m/s,\ v_2=2.6\ m/s`

The impulse the car experiences during that time is

`J=2498(2.6-17.1)=2498(-14.5)`

J=-36221 Kg.m/s

The magnitude of J is

J=36221 Kg.m/s