Help solving a physics problem?

Question

In order to pass a physical education class at a university, a student must run 1 mile in 12minutes. After running for 10 min, she still has 500 yd to go. If her maximum acceleration is 0.15m/s^2 can she make it? If the answer is no, determine what acceleration she would have to have to be successful.

Answer 1

A mile is also 1760 yards. Therefore, with 500 yards to go, her speed is (1760 yd - 500 yd) / (10 min) = 126 yd/min, assuming she has been traveling at a constant velocity. Then, use the formula x = (V_0)t + 0.5*at^2, where V_0 is 128 yd/min, t is 2 min, and a is given. If x is greater than 500 yd, the student was successful. If x is smaller than 500 yd, instead set x = 500 yd and solve for a while using all of the other known values.

You will need to convert all of these values into a consistent set of units; I'd recommend SI. You will need to use conversion factors, which are proportions that are equal to unity. For example, 1 yd = 0.914 m. Therefore, (0.914 m) / (1 yd) is a conversion factor. Using this with the 500 yd figure, I get (500 yd)(0.914 m / 1 yd) = 457 m, because yd cancels from the numerator and denominator.

Answer 2

Yes she can make it. The minimum required acceleration, assuming a constant acceleration and a constant velocity in the first 10 minutes is 0.031496 m/s^2 so the acceleration of 0.15 m/s^2 is greater than this by quite a bit so she should not have any problem making the one mile requirement. By the way, the constant velocity is 378 ft/min or 1.92024 m/s over the first 10 minutes and 3780 ft or 1130.1984 m.

Answer 3

so she has only 2 minutes to complete 500yard

1mile = 1,609.344m
500 yard = 457.2m
10 minutes = 600s

assume her speed is constant during the first 10 minutes.

find the speed after 10 minutes
(1,609.344 - 457.2)/600 = 1.92 m/s

so when she has 500 yard left, she's already traveling at 1.92m/s

Xf = .5at^2 + Vi + Xi
457.2 = .5(.15)t^2 + 1.92t + 0

.5(.15)t^2 + 1.92t - 457.2

use quadratic formula and you'll get t = 66.32s or 1.1minutes

so she does finish the race in time