Please help me solve the second distance.

Question

A drag racer can reach a speed of 53m/s over a distance of 120m. Over what distance can iy reach a speed of 85m/s?

Answer 1

v_f² = v_i² + 2ad is the kinematics equation we need to use to solve this one.

Assuming it starts from rest (it doesn't specifically say that but it's implied), v_i = 0 so our equation becomes

v_f² = v_i² + 2ad

53² = 0² + 2a(120)

2809 = 240a

11.7 m/s² = a

So the drag racer accelerates at a rate of 11.7 meters per second squared.

Assuming it's the same acceleration you can use the same equation to find the distance to reach a final velocity of 85 m/s

v_f² = v_i² + 2ad

85² = 0² + 2(11.7) d

7225 = 23.4 d

Solve for d and you'll find the distance