Question

A bicyclist is finishing her repair of a flat tire when a friend rides by with a constant speed of 4.8 m/s. Two seconds later the bicyclist hops on her bike and accelerates at 2.2 m/s2 until she catches up with her friend.

A. How much time, counting from the moment she hops on her bike, does it take until she catches up?

B. How far does she travel in this time?

Answer 1

Step-by-step explanation:

(4.8 m/s)t = 1/2(2.2 m/s²)t²

2(4.8 m/s)t / (2.2 m/s²) = t²

2(4.8 m/s) / (2.2 m/s²) = t²/t

t = 4.36 s

A. total time it takes to catch up to friend = 4.36s + 2s = 6.36s (took her 2 sec to hop on the bike and get going)

B. Distance she travels is the same distance the friend travels in 4.36 s = (4.8 m/s)(4.36 s) = 1/2(2.2 m/s²)(4.36 s)² = 20.9 m