6) A young woman named Katy Kool buys a super deluxe sports car that can acceler

Question

6) A young woman named Katy Kool buys a super deluxe sports car that can accelerate at the rate of 10ft/s She decides to test the car by dragging it with another speedster, Stan Speedy Both start from rest, but experienced Stan leaves Lascond before KathyI San constant acceleration of 8fus and Kathy maintains an acceleration of 1Oft/s, find a) the time it takes Kathy to overtake Stan, b)The distance she travels before she catches him, and c)the velocities of both cars at the instant she overtakes him

Explanation / Answer

Consider that after t seconds, Katy will overtake Stan. By the time Katy overtake Stan, both have traveled equal distance from the starting point.
Distance traveled by stan in t + 1 seconds, d = 0 x (t+1) + 1/2 a1 (t+1)2
Where a1 = 8 ft/s2
Distance traveled by Katy in t seconds, d = 0 x t + 1/2 a2 t2
Where a2 is the acceleration of Katy, a2 = 10 ft/s2.

Equating both the distances,
1/2 a1 (t+1)2 = 1/2 a2 t2
8 x (t+1)2 = 10 x t2
[(t+1)/t]2 = 1.25
Taking square root on both the sides,
(t+1)/t = 1.12
t + 1 = 1.12t
0.12t = 1
t = 8.47 s.

b)
Distance traveled, d = 1/2 a2 t2
= 0.5 x 10 x (8.47)2
= 358.89 ft

c)
Using the formula, v = u + at,
Katy's velocity after t seconds = 0 + a2 x t
= 10 x 8.47
= 84.72 ft/s

Stan's velocity after t + 1 seconds = 0 + a1 x (t+1)
= 8 x (8.47 + 1)
= 75.78 ft/s

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