Newton's Laws: Simple Constant Force Problem

[anastasiaw]

A car that weighs 12000.0 N is initially moving at a speed of 30.0 km/hr when the brakes are applied and the car is brought to a stop in 4.1 s. Find the magnitude of the force that stops the car, assuming it is constant.

Figured this one out, got: v0 = 8.33 m/s, a = -2.03 m/s^2, F = 2.49 X 10^3 N

What distance does the car move during this time?

This is the one I'm having trouble with.
Using: x(t) = x0 +v0*t + 1/2*a*t^2 and x0 = 0
x(t) = 0 + 8.33(4.6) + 1/2(-2.03)(4.6^2)
x(t) = 16.83 m

Tells me I am wrong. I don't know what to do from here.

 

[Feldoh]

"brought to a stop in 4.1 s"

x(4.6) = 0 + 8.33(4.6) + 1/2(-2.03)(4.6^2)

Maybe that's the problem XD

 

[latitude]

Sorry, is the time 4.6 s or 4.1 s?

EDIT: Got beat. LOL.

 

[anastasiaw]

Thanks... :)

17.1 m is the answer.

 

[nt07c]

How did you solve the first part? i have the same problem with different numbers and am having trouble with it.
Thanks

 

[anastasiaw]

The formula I used to calculate acceleration was:

a = (v - v0) / t

a is acceleration,
v is final velocity (should be 0 m/s),
v0 is initial velocity, which you must convert to m/s,
t is the time it takes to stop.


You can then use the very important equation

F = ma

to calculate the magnitude of the force that stops the car.

You will need to convert the weight given in Newtons to kilograms. You can do this using the same equation as above, with the acceleration in this equation as the acceleration due to gravity.