How far does Faith travel during the 30-second interval?

Question

Faith rides her bicycle with an initial velocity of 3.0 m/s for 20 seconds. She then begins to speed up with an acceleration of 0.40 m/s² for 10 seconds. How far does Faith travel during the 30-second interval?  (Round your answer to the nearest whole number. Do not include units in your answer.)

Answer 1

For both parts, we can use the equation Δx = v₀t+(1/2)at². Here, Δx is the distance that an object travels when it starts with a speed of v₀, travels for a time, t, and has an acceleration of a.

For the first part, v₀=3.0 m/s, t = 20 s, and a = 0. (Constant velocity means zero acceleration. This means Faith travels Δx = (3.0 m/s)(20 s) = 60 meters in the first 20 seconds.

For the second part, v₀=3.0 m/s, t = 10 s, and a = 0.40 m/s/s. This means that Faith travels

Δx = (3.0 m/s)(10 s) + (1/2)(0.4 m/s/s)(10 s)² = 50 m

In total, Faith travels 60 meters + 50 meters = 110 meters