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?
After you cross the finish line, you slow down and come to a stop, breathing hard. It takes you 10 seconds to come to a stop. What is your acceleration?

Answer 1

1) 1.08 m/s^2

Explanation:

Acceleration is equal to the change in velocity divided by the time taken:

$a=\frac{v-u}{\Delta t}$

where

v is the final velocity

u is the initial velocity

$\Delta t$ is the time taken

In this problem, we have:

- initial velocity: u = 0 (you start from rest)

- final velocity: v = 5.4 m/s

- time taken: $\Delta t = 5 s$

Therefore, the acceleration is

$a=\frac{v-u}{\Delta t}=\frac{5.4 m/s-0}{5 s}=1.08 m/s^2$

2) -0.54 m/s^2

We can calculate the acceleration to slow down using the same formula as before, but this time the data are as follows:

- initial velocity : u = 5.4 m/s

- final velocity : v = 0 (you come to a stop)

- time taken : $\Delta t = 10 s$

using the same formula, we find

$a=\frac{v-u}{\Delta t}=\frac{0-5.4 m/s}{10 s}=-0.54 m/s^2$

And the negative sign means it is a deceleration.