Jacky Catching Up with Davey: A Roller-Skating Adventure

To calculate the time it takes for Jacky to catch up with Davey, we need to consider the distance traveled by both Jacky and Davey. Davey is skating at a constant speed of 4m/s while Jacky accelerates uniformly at 2m/s.

Explanation:

Let Jacky takes t seconds to catch up with his friend. The distance traveled by him can be calculated using the formula s = ut + 1/2at². Since Jacky starts from rest, his initial velocity (u) is 0, and his acceleration (a) is 2m/s².

The distance covered by Davey while Jacky is still standing is 4(t + 2) since Davey skates for two seconds longer before Jacky starts to catch up. These two distances must be equal when Jacky catches up with Davey, so we can set up the equation:

4(t + 2) = 0.5 * 2 * t²

Solving the equation, we get: t² - 4t - 8 = 0

Using the quadratic formula, we find that t ≈ 5.46 seconds.