# If a person traveling at 40m/s increases speed to 60m/s in 12 seconds,what is the acceleration?

ishpiro | Certified Educator

The acceleration, by definition, is the rate of change of the velocity. In general case, when acceleration is not constant, it is determined by a small change in velocity over the small period of time. The average acceleration for a given time interval can be calculated as the difference of velocities in the beginning and the end of the interval, divided by the time interval.

In the given problem, the assumption seems to be that the acceleration is constant, and the person is traveling in the same direction throughout the time interval.  So the acceleration can be determined by dividing the difference of speeds by the time interval in which the change occurred:

`a = (Delta v)/(Delta t) = (v_2 - v_1)/(t_2 - t_1)`

In this case, the change of speed is

`Delta v = 60 m/s - 40 m/s = 20 m/s` .

The time interval is given to be 12 seconds, so the acceleration will be

`a = (20 m/s)/(12 s) = 1.67 m/s^2` .

The acceleration is 1/67 m/s^2.