What acceleration will stop the
car exactly at the stop sign?
vf^2 = vi^2 + 2aǻx
a = (vf^2 ívi^2 )/2ǻx
a = í144/72 m/s^2
a = í2.0 m/s^2
2.16 - Sample problem: a sprinter
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?
- Choose an appropriate equation based on the values you know and the one you want to find.
- 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.
vf^2 = vi^2 + 2aǻx
What is the runner's velocity at the
end of a 100-meter dash?
displacement ǻx = 100 m
acceleration a = 0.528 m/s 2
initial velocity vi = 0.00 m/s
final velocity vf