Physics question, will you catch your cab?

Question

The cab starts moving with an accelartion of 1 m/s^2 and is 20 meters down the street from you. You have 50 meters to catch the cab and are able to run with a max. speed of 8 m/s. Will you catch the cab given these circumstances?

Best Answer to first correct answer!!

Answer 1

Write an equation that gives your position as a function of time; and another equation that gives the cab's position as a function of time. Then set the two equations equal; and that will tell you at what time the two of you are at the same location (i.e., at what time (if any) you'll catch the cab.

Position of runner at any time t:
P_runner = (v)(t) = (8m/s)(t)

Position of cab at any time t:
P_cab = 20m + at²/2 = 20m + (1m/s²)t²/2

To catch the cab, P_runner must equal P_cab:
P_runner = P_cab
(8m/s)(t) = 20m + (1m/s²)t²/2

This is a quadratic equation, so use the quadratic formula to solve for "t". If there are any positive solutions that will yield P_runner < 50 m, then you can catch the cab. Otherwise, you can't.