You are driving in your car along a country road at a speed of 27.0m/s. As you c

Question

You are driving in your car along a country road at a speed of 27.0m/s. As you come over a crest of a hill, you notice a farm tractor 25.0m ahead of you on the road, moving in the same direction as you at a speed of 10.0m/s. You immediately slam on your brakes and slow down with a constant acceleration of magnitude 7.00m/s^2. Will you hit the tractor before you stop? How far will you travel before you collide with the tractor? If you stop, how far is the tractor in front of you when you finally stop?

Please show work. Thanks!

Explanation / Answer

The time that the car takes to stop is
t = v-u /a = 0-27 / (-7) = 3.86 second.
The distance covered by the car in time t is
s = ut + 1/2 at^2
s1 = 27t - 1/2*7t^2, = 52.07 m
The distance covered by the tractor in the same time t is
s2 = 25 + 10t = 63.6m
The difference in distance is
[s2 - s1] = 11.53m
The car will not hit the tractor.
The car will travel a distance 52.07 m before it stops .
The tractor is in front of the car at a distance of 11.53m when the car finally stops.

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