Question

An indy 500 driver is doing 105 m/s, with 100,000 meters and 10s left in a race. Her car can do a maximum acceleration of 15 m/s^2. Can she finish the race? Does she need to accelerate the entire time? If not, what is the minimum amount of time she must accelerate in order to finish the race in 10s?

Answer 1

LET ME KNOW IN THE COMMENTS IF THERE IS MISTYPING IN THE QUESTION.

Suppose she use max acceleration, then

a = 15 m/sec^2

Initial Velocity = 105 m/sec

time remaining = 10 sec

distance remaining = 100000 m

Using 2nd kinematic equation

d = U*t + 0.5*a*t^2

At max acceleration distance travelled will be

d = 105*10 + 0.5*15*10^2

d = 1800 m

So at max acceleration car can travel ONLY 1800 m, So she cannot finish this race.

Since she cannot finish this race, So part B is irrelevent

Part C

Again using 2nd kinematic equation

d = U*t + 0.5*a*t^2

100000 = 105*t + 0.5*15*t^2

7.5t^2 + 105t - 100000 = 0

Solving this quadratic equation

t = [-105 +/- sqrt (105^2 + 4*7.5*100000)]/(2*7.5)

taking positive sign

t = 108.7 sec = amount of time required

IF THIS ANSWER DOES NOT WORK THEN:

CHECK YOUR QUESTION AGAIN AND SEE THAT IF REMAINING DISTANCE IS 100000 METER IS CORRECT. AS 100000 m = 100 km, AND THERE IS NO CAR IN WORLD WHICH CAN TRAVEL 100 KM IN 10 SEC, AS FOR THIS TO COMPLETE CAR HAS TO TRAVEL AT 10 KM PER SECOND WHICH IS IMPOSSIBLE.

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