Question

A car is stopped for a traffic signal. When the light turns green, the car accelerates, increasing its speed from 0 to 5.10 m/s in 0.820 s. (a) What is the magnitude of the linear impulse experienced by a 66.0-kg passenger in the car during the time the car accelerates?

Answer 1

Answer:

$I=336.6kgm/s$

Explanation:

The equation for the linear impulse is as follows:

$I=F\Delta t$

where $I$ is impulse, $F$ is the force, and $\Delta t$ is the change in time.

The force, according to Newton's second law:

$F=ma$

and since $a=\frac{v_{f}-v_{i}}{\Delta t}$

the force will be:

$F=m(\frac{v_{f}-v_{i}}{\Delta t})$

replacing in the equation for impulse:

$I=m(\frac{v_{f}-v_{i}}{\Delta t})(\Delta t)$

we see that $\Delta t$ is canceled, so

$I=m(v_{f}-v_{i})$

And according to the problem $v_{i}=0m/s$, $v_{f}=5.10m/s$ and the mass of the passenger is $m=66kg$. Thus:

$I=(66kg)(5.10m/s-0m/s)$

$I=(66kg)(5.10m/s)$

$I=336.6kgm/s$

the magnitude of the linear impulse experienced the passenger is $336.6kgm/s$