You are asked to calculate the final velocity of a sprinter running a 100-meter dash. List the variables that you know and the one you are asked for, and then consider which equation you might use to solve the problem. You want an equation with just one unknown variable, which in this problem is the final velocity.

The sprinter’s initial velocity is not explicitly stated, but he starts motionless, so it is zero m/s.

Draw a diagram

Variables

What is the strategy?

1. Choose an appropriate equation based on the values you know and the one you want to find.
2. Enter the known values and solve for the final velocity.

Physics principles and equations

Based on the known and unknown values, the equation below is appropriate. We know all the variables in the equation except the one we are asked to find, so we can solve for it.

v_f² = v_i² + 2aΔx

Step-by-step solution

In step 4, we take the square root of 106 to find the final velocity. We chose the positive square root, since the runner is moving in the positive direction. When there are multiple roots, you look at the problem to determine the solution that makes sense given the circumstances. If the runner were running to the left, then a negative velocity would be the appropriate choice.