1. Final Velocity and Acceleration Equations
Physics Chapter 3C
Final Velocity and Acceleration Equations

2. Final Velocity after Acceleration
During acceleration, velocity changes
Equation for determining final velocity if initial velocity, time and acceleration are known:
Vf = Vi + at

3. Example
A ball rolling down an incline for 5.0 s undergoes a uniform acceleration of 4.2 m/s2. If the ball has an initial velocity of 2.0 m/s, what is the final velocity?
What we know:
Vi = 2.0 m/s, down
a = 4.2 m/s2, down
t = 5.0 s

4. Example continued Equation we will use:
vf = vi + at
Substitute values into the equation:
vf = 2.0 m/s + (4.2 m/s2)(5.0s)
Do the math!
Vf = 2.0 m/s m/s
Vf = 23 m/s, down
Check!
Make sure you have the right units, direction and sig dig!

5. Displacement during acceleration
Displacement is distance and direction from starting point
d = vt
If acceleration is uniform, displacement can be calculated using the equation:
D = (vf + vi) t 2

6. Displacement
If we do not know the final velocity, we can still find displacement:
d = vit + ½at2
Example (p 48)
A car starting from rest is accelerated at 6.1 m/s2 to the south. What is the car’s displacement during the first 7.0 s of acceleration?

7. What if we don’t know time?
We can calculate final velocity using the equation: Vf2 = vi2 + 2ad Example (p 49) An airplane must achieve a velocity of +71 m/s for takeoff. If the runway is 1.0 x 103 long, what must the acceleration be?