Problem with finding velocity in physics

Question

Can anyone help me with this question? I am stumped. Thanks

A car has a maximum acceleration of 1.15 x 10^4 miles/hour². If it starts from rest and accelerates as quickly as possible for 5.00 x 10² yards, what will its velocity be? (There are 1.760 x 10³ yards in a mile)

Answer 1

Use the kinematic equation of motion:

v_f² = v_i² + 2ax where v_f is the final velocity, v_i is the initial velocity, "a" is the acceleration, and "x" is the distance.

Since v_i = 0 (the car is at rest initially), we get:

v_f² = 2ax

But before we plug in the numbers, we have to have units that match up. To use miles/hour² we need the distance (x) to be in miles.

5.00x10² yard • 1 mile/1.760 x 10³ yards gives us x = 0.28409 miles

So v_f² = 2(1.15x10⁴)(0.28409) = 6534

To find v_f, take the square root of both sides to get v_f = 80.8 mi/hr