Chapter 1- Kinematics Regents Physics
One-Dimensional Motion - Constant Acceleration Equations
As we already know, acceleration is defined as the change of velocity per unit of time and can be found using: a= ∆v t
3990975151765 Since: ∆v= v f - v i , our formula then becomes:


If we apply some algebra and solve for " v f " then we arrive at:
v f = v i + at
Several derivations using the above information lead to useful equations when we want knowledge of an object\'s displacement, velocity, or acceleration at any particular time. Such equations include:
d = v i t + 1 2 at 2
v f 2 = v i 2 + 2ad
Knowing which equation to use relies simply on the information you are given in the problem. In other words, it is important to write down every piece of information given by the problem including the variable that you are looking for .
For example:
Roger starts from rest and accelerates at 4 m/s 2 for 3 seconds. How far has Roger travelled?




Notice how if an object starts from rest , v i (initial velocity) will always be zero. Similarly, if an object comes to rest , the v f (final velocity) will be zero.
A bowling ball moving 20 m/s comes to rest at the end of the alley 20 meters away. Determine the acceleration of the bowling ball.




A soccer ball kicked from rest travels 50 meters in 3 seconds. Determine the acceleration of the soccer ball.




A car is initially moving at 20 m/s. The car then accelerates at a rate of 5 m/s 2 . How fast will the car be moving after 400 meters?





5181600306070 Superman is flying at 300 m/s. He then accelerates at a rate of 20 m/s 2 for 10 seconds. How fast is he now flying?