Calculating Displacement with Negative Work

[Red_CCF]

I'm trying to figure out how to find the displacement when negative work is applied. I made the question myself so it could not make any sense at all, I'm just trying to understand a concept on my own.

Homework Statement

A car (2000kg) is moving at constant velocity at 4m/s to the right. It slows down to 1m/s in a time of 3s when an external force is applied against the car to the left. What is the displacement of the negative work?

Homework Equations

a=change in velocity/time
F=ma
W=Fd
Ek=1/2mv^2

The Attempt at a Solution

Using the above formulas I get an acceleration of -1m/s^2 (or 1m/s^2 left). This must mean that the force that opposes the motion of the car is -2000N (or 2000N left). The initial kinetic energy of the car is 16000J and the final kinetic energy is 1000J. The change in kinetic energy is 15000J so the work against the motion is -15000J? If so then the displacement is 7.5m? Would the displacement be positive or negative?

Thanks for any help that you can provide

 

[rock.freak667]

You did it correct, but you are off by a factor of 0.1. So recheck your calculations.

 

[PhanthomJay]

Negative work implies that the force vector and displacement vector colinear with the force vector are in opposite directions. If the force acting on the car is directed to the left in the negative direction, then the displacement must be to the ____? Or from a practical sense, while the car, moving initially to the right, then starts to slow down, in which direction is it moving (displacing) during that slowing down period?

 

[Red_CCF]

Negative work implies that the force vector and displacement vector colinear with the force vector are in opposite directions. If the force acting on the car is directed to the left in the negative direction, then the displacement must be to the ____? Or from a practical sense, while the car, moving initially to the right, then starts to slow down, in which direction is it moving (displacing) during that slowing down period?

If the force and displacement are in opposite directions, then the displacement must be towards the right, or am I tricking myself here because the object is accelerating to the left.

 

[Hootenanny]

If the force and displacement are in opposite directions, then the displacement must be towards the right, or am I tricking myself here because the object is accelerating to the left.

You are indeed correct!

 

[Red_CCF]

You are indeed correct!

Thanks! This was a confusing thing to wrap my head around because it's like pushing an object left but moving it right

 

[Hootenanny]

Thanks! This was a confusing thing to wrap my head around because it's like pushing an object left but moving it right

A good analogy to think about is when you're driving. If you press the brake pedal, then a force acts in the opposite direction of motion, slowing you down, but you are still moving forward.

 

[Red_CCF]

You did it correct, but you are off by a factor of 0.1. So recheck your calculations.

I fixed my error. So the actual answer should be 7.5m towards the right?