MotionMotion11.3 Acceleration11.3 Acceleration

Chapter 11Chapter 11

What are we going to learn?What are we going to learn?

►What is acceleration?What is acceleration?►How to calculate acceleration How to calculate acceleration

and interpret speed vs. time and interpret speed vs. time graphsgraphs

AccelerationAcceleration

►RateRate at which at which velocityvelocity changes changes

AccelerationAcceleration

►Can be described Can be described as as changeschanges in: in: speedspeed, , directiondirection, , or or both both

► It is a It is a vectorvector►2 types: 2 types: constantconstant and and free fallfree fall

►This This changechange may be due to either an may be due to either an increase or a decrease in increase or a decrease in speed speed

►PositivePositive: : increasingincreasing change in speed change in speed►NegativeNegative: : decreasingdecreasing change in speed change in speed

Acceleration AnimationAcceleration Animation

►http://www.physicsclassroom.com/mmhttp://www.physicsclassroom.com/mmedia/kinema/avd.cfmedia/kinema/avd.cfm

►http://www.physicsclassroom.com/http://www.physicsclassroom.com/mmedia/kinema/acceln.cfmmmedia/kinema/acceln.cfm

Constant AccelerationConstant Acceleration

►A A steady steady change in change in velocityvelocity

If the If the velocity velocity increases, the increases, the numeratornumerator is is positivepositive so so accelerationacceleration is positive is positive

If the velocity If the velocity decreasesdecreases, the numerator , the numerator isisnegativenegative so so accelerationacceleration is negative is negative

Change in velocity

Total timeAcceleration =

v vf i

t

Free FallFree Fall

►MovementMovement of an object of an object toward Earthtoward Earth solely solely because of because of gravitygravity

►Due to Due to change in speedchange in speed►RateRate of change in of change in speedspeed is 9.8 meters per is 9.8 meters per

second per second (second per second (9.8 m/s9.8 m/s22))

Changing DirectionChanging Direction

►AccelerationAcceleration may be due to its may be due to its direction direction constantly constantly changingchanging even though it is even though it is traveling at traveling at constant speedconstant speed

►Ex: horse on a carousel Ex: horse on a carousel

Changing Direction & SpeedChanging Direction & Speed

►Sometimes Sometimes motionmotion is changing in both is changing in both speed speed and and directiondirection at the same time at the same time

►Ex: skier on a downhill runEx: skier on a downhill run

Acceleration CalculationAcceleration Calculation

►Calculation for Calculation for straight-linestraight-line motion: divide motion: divide the the change in velocitychange in velocity by the by the total time total time

►This equation defines the This equation defines the averageaverage acceleration acceleration

►A A changechange in velocity by a in velocity by a constantconstant amount each amount each secondsecond (its (its positionposition changes changes by a constant by a constant amountamount each second) each second)

Acceleration GraphsAcceleration Graphs

►Acceleration is the slope of a speed-time Acceleration is the slope of a speed-time graphgraph

► In a In a linearlinear graph, the displayed data form graph, the displayed data form straight-linestraight-line parts parts

► In a In a nonlinearnonlinear graph, a graph, a curvecurve connects connects the data points that are plottedthe data points that are plotted

Instantaneous AccelerationInstantaneous Acceleration

►How fast a How fast a velocityvelocity is is changingchanging at a at a specific specific instantinstant

ExampleExample

►A snow skier is traveling at 15 m/s at one A snow skier is traveling at 15 m/s at one instant and at 22 m/s 2 seconds later. instant and at 22 m/s 2 seconds later. What is her acceleration? What is her acceleration?

► If she maintains this constant If she maintains this constant acceleration, how fast will she be acceleration, how fast will she be traveling one second later? traveling one second later?

Acceleration GraphAcceleration Graph

Questions...Questions...

Acceleration

is a change in

is measuredin units of

m/s2speed direction

►The rate at which velocity changes is The rate at which velocity changes is called called acceleration.acceleration.

► In terms of speed and direction, in what In terms of speed and direction, in what ways can an object accelerate? ways can an object accelerate?

Increase or decrease speed, change Increase or decrease speed, change direction, or both change speed and direction, or both change speed and direction.direction.

►Because acceleration is a quantity that Because acceleration is a quantity that has both magnitude and direction, it is has both magnitude and direction, it is a(n) a(n) vector.vector.

►True or false? Acceleration is the result ofTrue or false? Acceleration is the result ofincreases or decreases in speed. increases or decreases in speed. TrueTrue

► Ignoring air resistance, a rock in free fall Ignoring air resistance, a rock in free fall will have a velocity of will have a velocity of 39.2 m/s39.2 m/s after 4.0 after 4.0 seconds.seconds.

(9.8 m/s(9.8 m/s22)(4.0 s))(4.0 s)

►A horse on a carousel that is moving at a A horse on a carousel that is moving at a constant speed is accelerating because constant speed is accelerating because it it is constantly changing directionis constantly changing direction

►Write the equation used to calculate the Write the equation used to calculate the acceleration of an object . acceleration of an object .

►Acceleration = change in velocity divided Acceleration = change in velocity divided by the total time by the total time

►True or false? When the final velocity isTrue or false? When the final velocity isless than the initial velocity of an object, less than the initial velocity of an object, the acceleration is negative. the acceleration is negative. TrueTrue

►A skateboarder begins down a ramp at a A skateboarder begins down a ramp at a speed of 1.0 m/s. After 3 seconds, her speed of 1.0 m/s. After 3 seconds, her speed has increased to 4.0 m/s. Calculate speed has increased to 4.0 m/s. Calculate her acceleration.her acceleration.

a. 1.0 m/sa. 1.0 m/s22 b. 3.0 m/sb. 3.0 m/s22

c. 5.0 m/sc. 5.0 m/s22d. 9.8 m/sd. 9.8 m/s22

►Graph A represents the Graph A represents the motion of a downhill skier. How fast was motion of a downhill skier. How fast was the skier moving after traveling down the the skier moving after traveling down the hill for 2.5 seconds? hill for 2.5 seconds?

10 m/s10 m/s

► In which graph does an object move at In which graph does an object move at constant speed during the first 4 constant speed during the first 4 seconds? seconds?

Graph BGraph B

►Graph B represents the motion of a Graph B represents the motion of a mountain biker. What is the biker’s speed mountain biker. What is the biker’s speed at times of 10 s and 20 s? at times of 10 s and 20 s?

►Graph B represents the motion of a Graph B represents the motion of a mountain biker. What is the biker’s speed mountain biker. What is the biker’s speed at times of 10 s and 20 s? at times of 10 s and 20 s?

5 m/s5 m/s

0 m/s0 m/s

►Determine the acceleration of the Determine the acceleration of the mountain biker during the 10 second to mountain biker during the 10 second to 20 second time period. Show your work.20 second time period. Show your work.

0 m/s – 5 m/s 0 m/s – 5 m/s = = - 5 m/s- 5 m/s = -0.5 m/s = -0.5 m/s22

20 s – 10 s 10 s20 s – 10 s 10 s

►The plotted data points representing The plotted data points representing acceleration in a distance-time graph acceleration in a distance-time graph form a(n) form a(n) curved line.curved line.

►The measure of how fast a velocity is The measure of how fast a velocity is changing at a specific instant is known as changing at a specific instant is known as instantaneous acceleration.instantaneous acceleration.