# PHYS 2211 Module 3.3

## Average and Instantaneous Acceleration

3.3 Average and Instantaneous Acceleration

### Learning Objectives

By the end of this section, you will be able to:

• Calculate the average acceleration between two points in time.
• Calculate the instantaneous acceleration given the functional form of velocity.
• Explain the vector nature of instantaneous acceleration and velocity.
• Explain the difference between average acceleration and instantaneous acceleration.
• Find instantaneous acceleration at a specified time on a graph of velocity versus time.

### Acceleration

Average acceleration is the rate at which velocity changes:

Instantaneous acceleration is the acceleration at a specific point in time and is expressed mathematically as the derivative of the velocity function:

Practice!

Discuss!

Consider how you would answer these questions. Then bring this to class for a group discussion.

Estimate your acceleration if you run into a brick wall.

A car’s velocity as a function of time is given by v(t) = (3 m/s) + (0.1 m/s3)t2.

(a) Calculate the average acceleration for the time interval t = 0 to t = 5.00 s.

(b) Calculate the instantaneous acceleration for t = 0 s and t = 5.00 s.

(c) Draw v vs. t and a vs. t graphs for the car’s motion between t = 0 and t = 5.00 s.