Question

You are standing next to your friend, ready to race across a 100 meter field. When the go signal is given, you take 5 seconds to get to your maximum sprinting speed of 12 miles per hour (that’s about 5.4 meters per second). What is your acceleration, in meters per second squared?

Answer 1

The starting acceleration is 0 m/s and the ending is 5.4 m/s in the span of 5 seconds:

This will be: 5.4 m/s - 0 m/s and divided by 5 seconds

5.4-0/5= 5.4/5= 1.08

Acceleration= 1.08 m/s

Step-by-step explanation:

used an example from a text book

Answer 2

We can find the acceleration by using this formula

a= vf-vi/ t

To find the acceleration to reach the maximum velocity

`a = (5.4-0)/5`

`a = 1.08`. meters per second squared

We can find the distance coverted in first 5 seconds by following equation

s= vi t+ ½ at^2

`s = 1/2(1.08)(5)^(2)`

`s = 13.5`

He took 5 seconds to cover 13.5 meters and assuming he runs for the rest of the race at his maximum sprinting speed of 5.4 meters per seconds

`t = (s)/(v)`

`t = ((100-13.5))/(5.4)`

`t = 16.01`

Thus the total time to complete the race is

`T = 16.01 + 5 = 21.01`

Now we can find the acceleration of the complete 100 meter race by using the first equation.

`a = (5.4-0)/21.01`

`a = 0.25`

So the overall acceleration will be 0.25 meters per second squared.