Problem #4 A young woman named Kathy Kool buys a sports car that can accelerate

Question

Problem #4
A young woman named Kathy Kool buys a sports car that can accelerate at the rate of 4.90 m/s2. She decides to test the car by drag racing with another speedster, Stan Speedy. Both start from rest, but experienced Stan leaves the starting line 1.00 s before Kathy. If Stan moves with a constant acceleration of 3.50 m/s2 and Kathy maintains an acceleration of 4.90 m/s2, find
a) the time it takes Kathy to overtake Stan,
b) the distance she travels before she catches him, and
c) the speeds of both cars at the instant she overtakes him.
(of course, make sure you draw a position vs. time graph and a velocity vs. time graph first)

Explanation / Answer

A young woman named Kathy Kool buys a sports car that can accelerate at the rate of 4.90 m/s2. She decides to test the car by drag racing with another speedster, Stan Speedy. Both start from rest, but experienced Stan leaves the starting line 1.00s before Kathy. If Stan moves with a constant accerlation of 3.50 m/s2 and Kathy maintains an accerlation of 4.90 m/s2, what is the time it takes Kathy to overturn Stan. the distance she travels before she catches him, and the speeds of both cars at the instant she overtakes him. Stan Speedy’s acceleration is 3.5.m/s^2 Kathy Kool’s acceleration is 4.9 m/s^2. Both starts from rest. Stan Speedy takes t s Kathy Kool takes (t+1) s. 4.9 / 3.5 = {(t +1) / t)} ^2. Taking square root, 1.183 = (t +1) / t 0.183 t =1. t = 5.46s. Stan Speedy takes. 6.46s Kathy Kool takes. 5.46s Distance of meet = 0.5 x 3.5 x 6.46 x 6.46 = 73m Or 0.5 x 4.9 x 5.46 x 5.46 = 73m Speed of Stan Speedy= 3.5 x 6.46 = 22.61m/s Speed of Kathy Kool = 4.9 x 5.46 = 27.44.

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