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Expert: - 4/27/2009


Question
I need a little help on this homework question, i'd apreciate if you'd help... thank you.

A car drives in straight line at 80m/sec and brakes at a certain instant. The car accelerates at -20m/sec^2. How far will it go before it stops?

Answer
We know that the car starts at distance 0.

Acceleration is the derivative of velocity.
⌠
⌡-20 dt = -20t + C.
We know that C is 80, so the equation for speed is -20t + 80.
We can see that this is 0 { the car is stopped } when t=80/20=4.

Velocity is the derivative of distance.
⌠4
⌡0 -20t + 80 dt = (-10t² + 80t) from (0 to 4).

That is, -10(4²) + 80(4) - 0 = -160 + 320 = 160.

Note that when stopping a moving object at a constant -acceleration,
the distance the velocity would take you is always twice the distance of the deceleration.

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