Question

A car and driver weighing 6900 N passes a sign stating “Bridge Out 26.6 m Ahead.” She slams on the brakes, and the car decelerates at a constant rate of 10 m/s2 .

The acceleration of gravity is 9.8 m/s2 .
What is the magnitude of the work done stopping the car if the car just stops in time to avoid diving into the water?
Answer in units of J.

Answer 1

187286 J

Step-by-step explanation:

Lets work backwards. We are trying to find work, and are given kinematic variables. We know that the W = Fd, and since we already have d, all we need to find is F.

Using F = ma:

We know
`mg = W = 6900`, and so solving for m, we get 704.082kg.

Now we can plug in the decelleration of the car with the mass in order to find the force against the car(by the brake).

`F = 704.082*(-10) = -7040.82`

Now plugging this into W = Fd, we get:

`W = (7040.82)*26.6 = 187286J`

This is just the magnitude, but if you wanted to find the sign of W, you would use the fact that the force is going in the opposite direction of the car, so work would be negative. However, this question asks only for the magnitude, so we ignore the final sign.

Answer 2

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