400kJ of work is exerted to reduce a car's velocity

[WannabeEngineer]

Problem Statement: 4*10^5 Joules of work is required to reduce a car's velocity from 30m/s to 15m/s. What is the car's mass?

Relevant equations: Ke=.5*m*v^2

The attempt at a solution:

V1 = 30m/s
V2 = 15m/s
M = mass of car

.5*M*V1^2 - 4*10^5J = .5*M*V2^2

450M - 4*10^5J = 112.5M

-4*10^2 = -337.5M
1185kg = M

My Question: My algebra checks out I think, my only question is if I approached the problem correctly. The question is phrased in terms of work, so do I need to find force and displacement? Or is using the equation for kinetic energy acceptable?

Thanks guys

 

[haruspex]

Using KE is fine. You cannot readily use force and displacement because you have no idea how the force varies over time. It can be done, but it's unnecessary extra work.
It does bother me a bit that the question says a positive quantity of work has to be done to reduce the car's speed. It should be a negative quantity, of course.