2.2 Acceleration

Acceleration

p. 48-58

Objectives

The student will be able to:

• Describe motion in terms of changing velocity

• Compare graphical representations of accelerated and non-accelerated motions

• Apply kinematic equations to calculate distance, time, or velocity under conditions of constant acceleration

Acceleration

Acceleration: the rate of change of velocity

• Units: meters per second per second or meters per second squared (m/s2)

• Symbol: a

Average Acceleration Equation

average acceleration =

• Acceleration has both direction and magnitude.

Sample Problem 2B – p.49

As a shuttle bus comes to a normal stop, it slows down from 9.00 m/s to 0.00 m/s in 5.00s.

Find the average acceleration of the bus.

Problem Tip

Watch for implied data in problem statements, such as “starts at rest” (vi = 0 m/s) or “comes to rest” (vf = 0 m/s)

Practice 2B Problems

p.49 #1, 3-5

The signs of the velocity and acceleration combine to describe an object’s motion.

a Motion

+ + speeding up

_ _ speeding up

+ _ slowing down

_ + slowing down

- or + 0 constant velocity

0 - or + speeding up from rest

0 0 remaining at rest

Graphing Acceleration

On a velocity versus time graph, the slope of the line connecting one point and the next indicates the average acceleration.

slope

Acceleration Graph

Describe the acceleration at points A, B, C.

Think/Pair/Share

Conceptual Challenge on p.50

Constant Acceleration

What is it?

Demo - Walking

Deriving Displacement w/Constant Acceleration

What we know so far..

For objects moving with constant acceleration

avg. velocity =

Deriving Displacement w/Constant Acceleration

Displacement w/Constant Acceleration

displacement = (initial velocity + final velocity)(time interval)

• You will know that acceleration is constant by the phrase “uniform negative/positive acceleration”

Sample Problem 2C– p.53

A race car reaches a speed of 42 m/s. It then begins a uniform negative acceleration, using its parachute and braking system, and comes to rest 5.5 s later.

Find out how far the car moves while stopping.

Practice 2C Problems

p.53 #1, 3-5

Velocity with Constant AccelerationWhat if we don’t know the vf but we still want to calculate displacement…

=

Velocity with Constant Acceleration

final velocity = initial velocity + (acceleration · time interval)

Displacement w/Constant AccelerationWe can combine the previous equations:

and to form

Displacement w/Constant Acceleration

displacement = (initial velocity · time interval) +

acceleration · (time interval)2

Sample Problem 2D – p.55

A plane starting at rest at one end of a runway undergoes a uniform acceleration of 4.8 m/s2 for 15 s before takeoff.

What is its speed at takeoff?

How long must the runway be for the plane to be able to take off?

Practice 2D Problems

p.55 #1-3

So far all equations have required knowing the time interval.

If we don’t know t, we need to rearrange an equation and use substitution.

Rearrange for :

Then substitute into:

Final Velocity After any Displacement

• When you use this equation, you must take the square root of the equation to find the vf.

• The square root can be either positive or negative, you will determine which value is right by reasoning based on the direction of motion.

Sample Problem 2E – p.57

A person pushing a stroller starts from rest, uniformly accelerating at a rate of 0.500 m/s2.

What is the velocity of the stroller after it has traveled 4.75 m?

Practice 2E Problems

p.58 #1,3,5

Homework

p.70-71 #18-25