# A car can accelerate from 0 to 60 mph in 15 seconds. What is its acceleration?

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Acceleration is the rate of change of the velocity per unit time.

We are given that the velocity changes from 0mph to 60mph in 15 seconds. To find the average rate of change, take the difference in the velocities divided by the difference in time.

(`Delta v` is the change in velocity and `Delta t` is the change in time.)

`"Acceleration"=(Delta v)/(Delta t)=(60-0)/(15-0)=(4"mph")/("sec")`

We have a unit of time in the numerator and denominator (hours and seconds) so we can rewrite this in other units. In the U.S. we still frequently use the imperial system of measurements and acceleration is reported in `"ft"/"sec"^2` .

`4"mph"=(4"m")/"h"=(4"mi")/"h"*"h"/(3600"s")*(5280"ft")/"mi"=5.8bar(6)"ft"/"s"`

So `(4"mph")/s=5.8bar(6)"ft"/"s"^2`

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The SI unit for acceleration is `"m"/"s"^2` . 1ft=.3048m so:

`5.8bar(6)"ft"/"s"^2=5.8bar(6)*.3048 "m"/"s"^2=1.78816 "m"/"s"^2`

Acceleration is equivalent to the change in velocity over the change in time. In this problem, the units must be converted to feet per second.

60 * ` ``m/h` * 5280` ` `ft/m` * `1/3600` `h/s` = 88 `ft/s`

The units for miles and hours will cancel out leaving feet per second. 60 miles per hour is equivalent to 88 feet per second.

Now this value is taken over time to find the acceleration:

88`ft/s` `/` 15s = 88`ft/s` *` `` `` ` `1/15` * `1/s` = **5.867** feet per second squared.