Drag race problem Please label all variables and show formulas used. Two rather

Question

Drag race problem

Please label all variables and show formulas used.

Two rather unequal cars are competing in a drag race. For simplicity, let's assume that the accelerations of the cars are constant. Car 1 has an acceleration of 3.1 m/s^2, while Car 2 has an acceleration of 5.9 m/s^2. Car 2 gets off to a late start, 1.1 seconds after Car 1. At what time after Car 1 took off will it be overtaken by Car 2? How far down the track will this happen? How much faster will Car 2 be than Car 1 by that time?

Explanation / Answer

initial velocities of two cars are zero

Vo1 = Vo2 = 0 m/sec

a1 = 3.1 m/s^2

a2 = 5.9 m/s^2

for overtaking both the cars has to travel the same distance let's say that distance is S

time taken by car 1 is t sec to overtake,whereas the time taken by car2 is (t-1.1)

using kinematic equation S = (Vo*t)+(0.5*a*t^2)

S1 = S2 = S

(Vo1*t)+(0.5*a1*t^2) = (Vo2*(t+1.1))+(0.5*a2*(t-1.1)^2)

(0.5*3.1*t^2) = (0.5*5.9*(t-1.1)^2)

solving we get t = 4 sec

--------------------------------------------------------------

b) distance travellled by car1 is S1 = (0.5*a1*t^2) = (0.5*3.1*4^2) = 24.8 m

C) dV = V1 - V2 = (a2*t2)-(a1*t1)

dV = (5.9*(4-1.1))-(3.1*4)

dV = 4.71 m/sec

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