Question

If the sprinter accelerates at that rate for a distance of 15 m, and then maintains the velocity he has at that point for the remainder of the 100-m dash, what will be his time for the entire race?

Answer 1

The time for the entire race is 11.39 sec.

Step-by-step explanation:

Given that,

Distance = 15 m

Remainder distance = 100 m

Suppose A sprinter begins a race with an acceleration of 3.4 m/s².

We need to calculate the time

Using equation of motion

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

Put the value in the equation

`15=0+(1)/(2)*3.4* t^2`

`t^2=(30)/(3.4)`

`t=2.97\ sec`

We need to calculate the final velocity of sprinter

Using equation of motion again

`v=u+at`

Put the value into the formula

`v=0+3.4*2.97`

`v=10.09\ m/s`

We need to calculate the distance covers by sprinter

`d=100-15=85\ m`

The sprinter need to covers only 85 m.

We need to calculate the time

Using formula of time

`t=(d)/(v)`

Put the value into the formula

`t'=(85)/(10.09)`

`t'=8.42\ sec`

We need to calculate the time for the entire race

`t''=t+t'`

Put the value into the formula

`t''=2.97+8.42`

`t''=11.39\ sec`

Hence, The time for the entire race is 11.39 sec.