How far does the car travel while slowing down?

[StephenDoty]

A 1000.0 kg car experiences a net force of 9500N while decelerating from 30.0m/s to 23.4m/s. How far does the car travel while slowing down?

I do not even know how to start to setup the problem. I know that W=Fd but I do not know how to apply this with the velocities.

Any help would be appreciated. Thank you.

Stephen

 

[PhanthomJay]

You can calculate the car's acceleration from the given data using Newton's laws, then use the standard kinematic equations of motion to calculate the distance.

 

[StephenDoty]

since we are on the energy and momentum chapter is there any way to do it with KE and PE?

 

[PhanthomJay]

since we are on the energy and momentum chapter is there any way to do it with KE and PE?

Oh, sure. Use the work energy theorem
$$W_{total} = W_{net} = \Delta KE$$. In general , you've got to be a bit careful when using this equation, because W_net includes work done by both conservative (like gravity) and non-conservative (friction, etc.) forces, but it this case, those forces are given as one net number, so you don't have to worry about PE change.

 

[StephenDoty]

so...
Fd=1/2mvf^2 - 1/2mvi^2

?

 

[PhanthomJay]

so...
Fd=1/2mvf^2 - 1/2mvi^2

?

yes, where the value you use for F is the given F_net. Check it out both ways using the energy method vs. Newton 2 and the kinematic equations.

 

[StephenDoty]

Would vi be 23.4m/s
and vf= 30m/s
?

If it is the other way around then F*D= a negative number

any help would be appreciated.

 

[subwaybusker]

vf is 23.4m/s since you're slowing down, right? so the change in kinetic you get should be a negative number, and keep in mind that the force of friction is always negative, so the work done is negative too.

 

[StephenDoty]

so vi= 30.0m/s
vf=23.4m/s

and the force of 9500N is negative?

-9500N*d=(1/2)(1000kg)(23.4m/s)^2 - (1/2)(1000kg)(30m/s)^2

?

 

[subwaybusker]

yep.

 

[StephenDoty]

d= 18.5m or 19m with sig figs.?

 

[Snazzy]

A general rule of thumb is to use the least amount of sig figs as the values given to you in the question.

 

[StephenDoty]

which would be 2 from 9500N

 

[StephenDoty]

do i have the right number of sig figs