02 Lecture Slides

Copyright © 2012 Pearson Education Inc.

PowerPoint® Lectures forUniversity Physics, Thirteenth Edition – Hugh D. Young and Roger A. Freedman

Lectures by Wayne Anderson

Chapter 2

Motion Along a Straight Line


Goals for Chapter 2• To describe straight-line motion in terms of velocity and

acceleration

• To distinguish between average and instantaneous velocity and average and instantaneous acceleration

• To interpret graphs of position versus time, velocity versus time, and acceleration versus time for straight-line motion

• To understand straight-line motion with constant acceleration

• To examine freely falling bodies

• To analyze straight-line motion when the acceleration is not constant


Introduction• Kinematics is the study of motion.

• Velocity and acceleration are important physical quantities.

• A bungee jumper speeds up during the first part of his fall and then slows to a halt.

Bryan Spencer

If picture is changed to 13e opener of a bungee jumper, then the picture won't match lecture text.


Displacement, time, and average velocity—Figure 2.1

• A particle moving along the x-axis has a coordinate x.

• The change in the particle’s coordinate is x = x2 x1.

• The average x-velocity of the particle is vav-x = x/t.

• Figure 2.1 illustrates how these quantities are related.


Negative velocity

• The average x-velocity is negative during a time interval if the particle moves in the negative x-direction for that time interval. Figure 2.2 illustrates this situation.


A position-time graph—Figure 2.3

• A position-time graph (an x-t graph) shows the particle’s position x as a function of time t.

• Figure 2.3 shows how the average x-velocity is related to the slope of an x-t graph.


Instantaneous velocity—Figure 2.4

• The instantaneous velocity is the velocity at a specific instant of time or specific point along the path and is given by vx = dx/dt.

• The average speed is not the magnitude of the average velocity!


Average and instantaneous velocities• In Example 2.1, the cheetah’s instantaneous velocity

increases with time. (Follow Example 2.1)


Finding velocity on an x-t graph

• At any point on an x-t graph, the instantaneous x-velocity is equal to the slope of the tangent to the curve at that point.


Motion diagrams• A motion diagram shows the position of a particle at

various instants, and arrows represent its velocity at each instant.

• Figure 2.8 shows the x-t graph and the motion diagram for a moving particle.


Average acceleration• Acceleration describes the rate of change of velocity with time.

• The average x-acceleration is aav-x = vx/t.

• Follow Example 2.2 for an astronaut.


Instantaneous acceleration• The instantaneous acceleration is ax = dvx/dt.

• Follow Example 2.3, which illustrates an accelerating racing car.


Finding acceleration on a vx-t graph

• As shown in Figure 2.12, the x-t graph may be used to find the instantaneous acceleration and the average acceleration.


A vx-t graph and a motion diagram

• Figure 2.13 shows the vx-t graph and the motion diagram for a particle.


An x-t graph and a motion diagram

• Figure 2.14 shows the x-t graph and the motion diagram for a particle.


Motion with constant acceleration—Figures 2.15 and 2.17

• For a particle with constant acceleration, the velocity changes at the same rate throughout the motion.


The equations of motion with constant acceleration

• The four equations shown to the right apply to any straight-line motion with constant acceleration ax.

• Follow the steps in Problem-Solving Strategy 2.1.

vx v0x axt

xx0v0xt12axt2

vx2 v0x

2 2ax x x0

x x0 v0x vx

2

t


A motorcycle with constant acceleration

• Follow Example 2.4 for an accelerating motorcycle.


Two bodies with different accelerations

• Follow Example 2.5 in which the police officer and motorist have different accelerations.


Freely falling bodies

• Free fall is the motion of an object under the influence of only gravity.

• In the figure, a strobe light flashes with equal time intervals between flashes.

• The velocity change is the same in each time interval, so the acceleration is constant.


A freely falling coin

• Aristotle thought that heavy bodies fall faster than light ones, but Galileo showed that all bodies fall at the same rate.

• If there is no air resistance, the downward acceleration of any freely falling object is g = 9.8 m/s2 = 32 ft/s2.

• Follow Example 2.6 for a coin dropped from the Leaning Tower of Pisa.


Up-and-down motion in free fall

• An object is in free fall even when it is moving upward.

• Follow Example 2.7 for up-and-down motion.


Is the acceleration zero at the highest point?—Figure 2.25

• The vertical velocity, but not the acceleration, is zero at the highest point.


Two solutions or one?

• We return to the ball in the previous example.

• How many solutions make physical sense?

• Follow Example 2.8.


Velocity and position by integration

• The acceleration of a car is not always constant.

• The motion may be integrated over many small time intervals to give .00 0

and t t

x ox x xv v a dt x x v dt


Motion with changing acceleration

• Follow Example 2.9.

• Figure 2.29 illustrates the motion graphically.

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