Acceleration Formula

Acceleration is a measure of how quickly the velocity of an object changes. So, the acceleration is the change in the velocity, divided by the time. Acceleration has a magnitude (a value) and a direction. The direction of the acceleration does not have to be the same as the direction of the velocity. The units for acceleration are meters per second squared (m/s²).

a = acceleration (m/s²)

v_f = the final velocity (m/s)

v_i = the initial velocity (m/s)

t = the time in which the change occurs (s)

Δv = short form for "the change in" velocity (m/s)

1) A sports car is travelling at a constant velocity v = 5.00 m/s. The driver steps on the gas, and the car accelerates forward. After 10.0 seconds, the driver stops accelerating and maintains a constant velocity v = 25.0 m/s. What was the car’s acceleration?

Answer: The initial velocity is v_i = 5.00 m/s, in the forward direction. The final velocity is v_f = 25.0 m/s in the forward direction. The time in which this change occurred is 10.0 s. The acceleration is in the forward direction, with a value:

The car's acceleration is 2.00 m/s², forward.

2) A child drops a rock off of a cliff. The rock falls for 15.0 s before hitting the ground. The acceleration due to gravity is g = 9.80 m/s². What was the velocity of the rock the instant before it hit the ground?

Answer: The rock was released from rest, so the initial velocity is v_i = 0.00 m/s. The time in which the change occurred is 15.0 s. The acceleration is 9.80 m/s². The final velocity must be found, so rearrange the equation:

v_f = v_i + at

v_f = 0.00 m/s +(9.80 m/s²)(15.0 s)

v_f = 147 m/s

The rock is falling, so the direction of the velocity is down.