# Acceleration

Acceleration is a vector quantity that is defined as the rate at which an object changes its velocity. An object is accelerating if it is changing its velocity. Acceleration has to do with changing how fast an object is moving. If an object is not changing its velocity, then the object is not accelerating.

## Constant Acceleration:

Sometimes an accelerating object will change its velocity by the same amount each second. This is referred to as a constant acceleration since the velocity is changing by a constant amount each second.

An object with a constant acceleration should not be confused with an object with a constant velocity. If an object is changing its velocity – whether by a constant amount or a varying amount – then it is an accelerating object. And an object with a constant velocity is not accelerating.

## Equations:

Acceleration = a = (Vf – Vi)/ time

Acceleration is a vector quantity, therefore, it has a direction. The direction of the acceleration vector depends on two things:

• whether the object is speeding up or slowing down
• whether the object is moving in the + or – direction

The general principle, which can be applied to any direction the object is traveling, for determining the acceleration is:

If an object is slowing down, then its acceleration is in the opposite direction of its motion.

## Practice problems:

1. When a bus comes to a sudden stop to avoid hitting a dog, it slows from 9.00 m/s to 0.00 m/s in 1.50 seconds. Find the average acceleration of the bus

Change in velocity = Vf – Vi = 0 – 9 = -9 m/s

Time taken = 1.5 sec

Average acceleration = (Vf – Vi)/ time = -9 / 1.5 = 6 m/s2

2. A car traveling initially at 7.0 m/s accelerates to velocity of 12.0 m/s in 2.0 s. What is the average acceleration of the car?

Change in velocity = Vf – Vi = 12 – 7 = 5 m/s

Time taken = 2 sec

Average acceleration = (Vf – Vi) / time = 5/2 = 2.5 m/s2

3. With an average acceleration of 0.50 m/s2, how long will it take a cyclist starting from rest to reach 13.5 m/s?

Change in velocity = Vf – Vi = 13.5 – 0 = 13.5 m/s

a = 0.50 m/s2

t = ? (solve)

Average acceleration = (Vf – Vi) / time

0.50 = 13.5 / t

t * 0.50 = 13.5

t = 13.5 / 0.50

t = 27 sec

Reference

https://www.physicsclassroom.com/class/1DKin/Lesson-1/Acceleration