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

`I=336.6kgm/s`

Step-by-step 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=(v_(f)-v_(i))/(\Delta t)`

the force will be:

`F=m((v_(f)-v_(i))/(\Delta t))`

replacing in the equation for impulse:

`I=m((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`