Question

In a quarter-mile drag race, two cars start simultaneously from
rest, and each accelerates at a constant rate until it either
reaches its maximum speed or crosses the finish line. Car A has an
acceleration of 10.6 m/s^{2} and a maximum speed of 104
m/s. Car B has an acceleration of 11.7 m/s^{2} and a
maximum speed of 87.5 m/s. **(a)** Which car wins the
race? **(b)** By how many seconds does this car win
the race?

Answer #1

d = 1609/4 = 402.25 m

For Car A:

during accelerated motion:

vf = vi + a t

104 = 0 + 10.6 t1

t1 = 9.811 sec

distance travelled in this time, d1 = v0 t + at^2 /2

d1 = 510.2 m

so it will cross the distance during this time.

402.25 = 0 + 10.6 t^2 /2

tA = 8.712 sec

For car B:

t1 = 87.5 / 11.7 = 7.48 sec

87.5^2 - 0^2 = 2(11.7) (d1)

d1 = 327.2 m

d2 = d - d1 = 75.05 m

t2 = 75.05 / 87.5 = 0.858 sec

tB = t1 + t2 = 8.34 sec

hence car B will win race: .......Ans

(B) delta(t) = tA - tB = 0.374 sec .......Ans

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