Question

Kathy tests her new sports car by racing with Stan, an experienced racer. Both start from rest, but Kathy leaves the starting line 1.00 s after Stan does. Stan moves with a constant acceleration of 3.50 $\frac{m}{s^{2}}$ while Kathy maintains an acceleration of 4.90 $\frac{m}{s^{2}}$ . Find:

A) the time at which Kathy overtakes Stan.

B) the distance at which she travels before she catches him.

C) the speeds of both cars at the instant Kathy over takes Stan.

Answer 1

Answer: a) Kathy overtakes Stan when their positions match 4.90 m/-1.006.46 or 0.54124 The smaller time occurs before Kathv starts, where the quadratic equation for za@ does not hold rk(tくM4-0, as Kathy is sitting at the starting line). Therefore, the Kathy passes Stan at the larger timet 6.46 s (measured since Stan left the starting line) (b) Kathy travels the same distance as Stan 7,4,) = ה ,t2 (3.50 m/s2) . (6.46 s)2-73.0 m Symbolically, asak c) The velocities at the passing point are v,(tz)-atp (3.50 m/s) (6.46 s) 226 m/s n(,)-a2(, . Д) (4.90 m/s) . (6.46 s-1.00 s)-26.7 m/s