How would you work this problem out?

Question

Physics 1 Review Question 1

An athlete running 2.6 m/s increases his velocity to 3.7 m/s in 2.7 s. What is the acceleration of the runner? Round your answer to the nearest hundredth. 

Answer 1

This is a question under the concept of acceleration being the rate of change of velocity.

Stated mathematically:

a = Δv / Δt = ( v_f - v_i ) / ( t_f - t_i )

The technical version of the denominator is usually replaced by the time passed t like so:

a = ( v_f - v_i ) / t

But do note that the first equation applies in generally all cases of constant acceleration for some period of time between t_i and t_f.

The runner begins at 2.6 m / s and ends at 3.7 m / s in those 2.7 s. So your variables would be assigned as follows:

v_i = 2.6 m / s v_f = 3.7 m / s t = 2.7 s

Inputting these into the equation looks like:

a = ( 3.7 m / s - 2.6 m / s ) / ( 2.7 s ) = ( 1.1 m / s ) / ( 2.7 s )

a ≈ 0.41 m / s²

I hope this helps!