Question

A bicyclist is finishing his repair of a flat tire when a friend rides by with a constant speed of 3.1 m/s . Two seconds later the bicyclist hops on his bike and accelerates at 2.4 m/s^2 until he catches his friend. How much time does it take until he catches his friend (after his friend passes him)?

Answer 1

It will take approximately 1.61 seconds for the bicyclist to catch up to his friend after his friend passes him.

Step-by-step explanation:

To determine the time it takes for the bicyclist to catch up to his friend, we can use the equation:

distance = initial velocity * time + 0.5 * acceleration * time^2

Since the friend is traveling at a constant speed of 3.1 m/s, the distance traveled by the bicyclist during the 2-second delay is 6.2 m. Using the equation above:

6.2 m = 0 m/s * t + 0.5 * 2.4 m/s^2 * t^2

Simplifying the equation:

2.4 m/s^2 * t^2 = 6.2 m

t^2 = 6.2 m / 2.4 m/s^2

t^2 = 2.5833 s^2

t ∼ 1.61 s

Therefore, it will take approximately 1.61 seconds for the bicyclist to catch up to his friend.