# Thinkwell | Exercise 3.1.pdf - Thinkwell | Exercise...

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10/27/19, 9:26 PM Thinkwell | Exercise1 of 10 next Ken is driving down the road when a car suddenly pulls out in front of him. He applies the brake sharply and his car goes into a skid. While the car skids, it decelerates at a constant rate of 15
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meters /sec2 . If the car skids for 80 meters before stopping, how fast was Ken driving before he hit the brakes?
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Unformatted text preview:- 15 (0) + C = v C = v . Then v (t) =- 15 t+ v. Now we can integrate again to find the position function p (t) = ∫ v ( t ) dt. = ∫ (-15t + v ) dt=-15⋅ + v t + C =-t 2 + v t + C Since the car has not skid at all at t = 0, we have p(0) = 0, so thatt 22 15 2 1510/27/19, 9 : 26 PM Thinkwell | ExercisePage 2 of 2 answer keynext- (0) 2 + v(0) +C = 0, C = 0. Then p ( t) =- t 2 + vt .Ok, now comes the hard part. Let t s be thetime that the car finishes its skid. We know that the car skids for 80 meters, sop ( t s ) =-t s 2 + v t s = 80. We also know that when the car finishes its skid, it is motionless. v ( t s ) =-15t s + v = 0 Solving these two equations for v gives usv ≈ 49 meters/sec. 15 2 15 2 152