PHYS 2211 Module 3.2

Instantaneous Velocity and Speed

Recommended Reading

3.2 Instantaneous Velocity and Speed

Learning Objectives

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

  • Explain the difference between average velocity and instantaneous velocity.
  • Describe the difference between velocity and speed.
  • Calculate the instantaneous velocity given the mathematical equation for the velocity.
  • Calculate the speed given the instantaneous velocity.

Speed and Velocity

Pause and Predict 3.2.1
A ball, initially at the 1 m mark, moves 5 m in the positive x direction in 2.0 s. It then moves 3 m in the negative x direction in 1.5 s. Then it moves 7 m in the positive x direction in 3.0 s. What are the average speed and average velocity of the ball over the entire trip?
(a) 6.8 m/s, 2.8 m/s
(b) 2.3 m/s, 1.4 m/s
(c) 2.8 m/s, 1.5 m/s
(d) 2.3 m/s, 2.8 m/s
(e) 6.8 m/s, 1.4 m/s
Pause and Predict 3.2.2
The graph shows the motion of a ball that moves 10 m in the +x direction in 2 s. The ball stays at that position for 2 s before moving 4 m in the -x direction in 2 s. Then the ball stops. What is the ball’s velocity at the instant of t = 5 s?
(a) 1.6 m/s
(b) -1.6 m/s
(c) 2.0 m/s
(d) -2.0 m/s
(e) 0 m/s

Instantaneous Velocity

Quick Calculus Review

Practice!

Practice 3.2.1

This position versus time graph exhibits what kind of motion?
(a) An object at rest.
(b) A moving object that is speeding up.
(c) An object moving at a constant speed.
(d) A moving object that is slowing down.
Practice 3.2.2

This position versus time graph exhibits what kind of motion?
(a) An object at rest.
(b) A moving object that is speeding up.
(c) An object moving at a constant speed.
(d) A moving object that is slowing down.
Practice 3.2.3

This position versus time graph exhibits what kind of motion?
(a) An object at rest.
(b) A moving object that is speeding up.
(c) An object moving at a constant speed.
(d) A moving object that is slowing down.

Discuss!

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

Suppose a particle moves along the x-axis. Its x-coordinate varies with time according to the expression x(t) = 8 + 3.8t + 2.5t2, where x is in meters and t is in seconds.

(a) Determine the displacement Δx of the particle in the time interval t = 9 s to t = 20 s.

(b) Calculate the average velocity in the time interval t = 9 s to t = 20 s.

(c) Find the instantaneous velocity of the particle at t = 18.4 s.