Finding Time, given velocity and acceleration

[bustin]

Homework Statement

A bicyclist is finishing his repair of a flat tire when a friend rides by with a constant speed of 3.9 m/s. Two seconds later the bicyclist hops on his bike and accelerates at 2.0 m/s^{2} until he catches his friend.

Homework Equations

V=V0+At

The Attempt at a Solution

Well I could put the numbers in the equation but I know its wrong anyways. Not sure how to get this problem going.

 

[Delphi51]

You need distance formulas because the distance traveled is the same in both cases.
Don't forget to account for the 2 second delay. You might want to put t in one formula and t-2 in the other.

 

[nlightner]

I would approach this problem by first defining the variables and their units. The velocity of the friend is given as 3.9 m/s, and the acceleration of the bicyclist is given as 2.0 m/s^2. The time it takes for the bicyclist to catch his friend is unknown and will be represented by t.

Next, I would use the kinematic equation V = V0 + at to solve for time. In this case, the initial velocity (V0) is 0 m/s since the bicyclist was initially stationary before accelerating. Therefore, the equation becomes 3.9 m/s = 0 m/s + 2.0 m/s^2 * t.

Solving for t, we get t = 3.9 m/s / 2.0 m/s^2 = 1.95 seconds. This means it takes the bicyclist 1.95 seconds to catch up to his friend.

Finally, I would double check my answer and consider any potential limitations or assumptions made in solving this problem. For example, we assumed that the bicyclist and his friend are moving in a straight line and that there are no external forces acting on them. Overall, I would present my solution with the appropriate units and any relevant explanations or considerations.