Topic 1.3

constant velocity uniform motion changing velocity accelerated motion

Any change in velocity … Speeding up Slowing down Changing direction

We define acceleration as …

… the exact acceleration when the acceleration is uniform … the average acceleration when it isn’t Since we are using the same formula regardless of whether or not the acceleration is uniform we are not going to make a big deal of differentiating between the exact and average acceleration.

Sample Problem A car accelerates at a constant rate from 40 km/h[E] to 90 km/h[E] in 5.0s. What is its acceleration? Every second the velocity increases by 10 km/h towards the East [E] is +ive

Sample Problem A car accelerates at a constant rate from 40 km/h[E] to 90 km/h[E] in 5.0s. What is its acceleration? Every second the velocity increases by 2.8 m/s towards the East [E] is +ive

Sample Problem A runner starting from rest reaches a velocity of 9.6 m/s in 2.0s. What is her average acceleration? Assume she runs in the +ive direction Every second the velocity increases by 4.8 m/s

Sample Problem A baseball player running at 8.0m/s[W] slides into third base, coming to rest in 1.6s. What is his average acceleration? [w] is +ive Slowing down as you go west is the same as speeding up towards the east

Practice Topic 1.3 Acceleration (Handout #1)

Assignment

the slope of the line on a d-t graph Recall, straight line on a d-t graph means … … Uniform Motion or Constant Velocity

Graphing Motion + Time (s) Velocity (m/s)

Straight line on a v-t graph means… …Uniform or constant acceleration

Sample Problem Determine the object’s acceleration for …

a) the first 8s

b) from 8s to 12s

Sample Problem A B C Determine the acceleration for each lettered section.

A B C A:

A B C B:

A B C C:

Practice Topic 1.3 Acceleration (Handout #2)

Assignment 2

Sample Problem The graph shows the motion of a car for a 10s interval. What is the displacement of the car during this time interval?

Consider the rectangle formed by the graph line and time axis Length = 10s Width = 20m/s The displacement in any time interval is given by the area under the v-t graph

Check out IntArea/IA.htmlhttp:// IntArea/IA.html 01/mechanics/motion-in-1d/area-under-v- vs-t-curve-texthttp:// 01/mechanics/motion-in-1d/area-under-v- vs-t-curve-text

The graph shows the velocity of a ball that starts from rest and rolls down a long hill. What is the ball’s displacement after 10s? Base=10s Height=20m/s

The graph shows the motion of a dog running up and down a straight road for a 16s interval. What is the dogs displacement over that time interval?

Practice Topic 1.3 Acceleration (Handout #3)

Assignment 3

Uniform Motion

Equations of Motion with Uniform Acceleration

Recall

Sub [1] into [2]

Bodies in Free Fall Free fall refers to any body falling under the influence of gravity alone That is, the only force that acts on a freely falling object is gravity

How do things fall? Aristotle ( BC) said that objects would fall at a constant speed and that the speed of a falling object would be proportional to its mass That is, a 2kg stone would fall twice as fast as a 1kg stone This went unchallenged for nearly 2000 years

Galileo (1564 – 1642) hypothesized that objects do not fall at a constant speed, but accelerate He conducted experiments using balls rolled down inclined planes and a water clock He concluded that objects in free fall undergo uniform acceleration He also concluded that in the absence of air resistance the acceleration of a freely falling body is independent of mass

Near the surface of the earth the acceleration due to gravity, denoted g, is … g = 9.8m/s 2 It varies slightly from location to location due to: –elevation –latitude –topography –geology

Since freely falling bodies experience uniform acceleration, the equations we derived earlier also apply when solving free fall problems