Question

One simple model for a person running the 100m dash is to assume the sprinter runs with constant acceleration until reaching top speed, then maintains that speed through the finish line.

If a sprinter reaches his top speed of 11.3m/s in 2.44s , what will be his total time?

Answer 1

Step-by-step explanation:

Given

Race length
`L=100\ m`

Runner reaches maximum velocity in
`t_1=2.4\ s`

`v_(max)=11.3\ m/s`

distance traveled during this time

`v=u+at`

`11.3=0+a* 2.4`

`a=(11.3)/(2.4)=4.708\ m/s^2`

distance traveled in this time

`s=ut+(1)/(2)at^2`

`s=0+0.5* 4.708* (2.44)^2`

`s=14.014\ m`

Remaining distance will be traveled with
`v_(max)`

remaining distance
`d=100-14.014=85.98\ m`

time taken
`t_2=(d)/(v_(max))=(85.98)/(11.3)=7.609\ s`

total time
`t=t_1+t_2`

`t=2.44+7.609=10.049\ s`