## A dog runs down his driveway with an initial speed of 5 m/s for 9 seconds, then uniformly increases his speed to 10 m/s in 5 seconds.?

How long is his driveway?

I have my answer and I got my answer using the equation Δx = 1/2(Vo + Vf)t.

I got 97.5 meters however my teacher tells me its 77.5 meters. She isn’t that great of a teacher and she’s teaching AP Physics with a pre-med degree… Can someone with great experience give me a second opinion? Feel free to call me out if I’m wrong.

## Answer ( 1 )

There are two steps to solve this problem. When the dog is running at a constant speed, use the following equation.

d = v * t = 5 * 9 = 45 meters

When the speed is changing, use the following equation

d = ½ * (vi + vf) * t

d= ½ * (5 + 10) * 5 = 37.5 meters

Total distance = 45 + 37.5 = 82.5 meters

OR

d = vi * t + ½ * a * t^2

a = (vf – vf) ÷ t

a = (10 – 5) ÷ 5 = 1 m/s^2

d = 5 * 5 + ½ * 1 * 5^2 = 37.5 meters