Question

Jim is trying to improve his speed on the track so he can qualify for the State Championships. As he is running, he goes from 70 meters/minute (beginning speed) to 106 meters/minute (final speed) in 9 seconds. What is his acceleration?

Answer 1

His acceleration is
`(1)/(15)` meters per seconds²

Explanation:

Acceleration is the rate of change of the speed

The formula of acceleration is
`a=(v_(f)-v_(i))/(t)` , where

• 
  `v_(f)` is the final speed
• 
  `v_(i)` is the initial speed
• The unit of the acceleration is meters/second²

∵ Jim goes from 70 meters/minute (beginning speed) to

106 meters/minute (final speed) in 9 seconds

∴ His initial speed
`v_(i)` = 70 meters/minute

- Change it the meter per second

∵ 1 minute = 60 seconds

∴
`(70)/((1)(60))=(70)/(60)=(7)/(6)` meters/second

∴
`v_(i)` =
`(7)/(6)` meters/second

∵ His final speed
`v_(f)` = 106 meters/minute

- Change it the meter per second

∴
`(106)/((1)(60))=(106)/(60)=(53)/(30)` meters/second

∴
`v_(f)` =
`(53)/(30)` meters/second

∵ The time of the change of his speed is 9 seconds

∴ t = 9

∵ The formula of acceleration is
`a=(v_(f)-v_(i))/(t)`

- Substitute the values of t,
`v_(i)` and
`v_(f)` in the formula above

∴
`a=((53)/(30)-(7)/(6))/(9)=(1)/(15)`

∴ His acceleration is
`(1)/(15)` meters per seconds²