Name:________________________________ Date:____________ Period: _____

Unit 2: Motion Section 3: Acceleration

Learning Goals Define acceleration. Determine acceleration by mathematical and graphical means. Explain the role of acceleration in describing curved motion and objects in free

fall.

AccelerationAcceleration is the rate at which your speed (or velocity) changes.

Example: If your speed increases by 1 meter per second (m/s) for each second, then your acceleration is 1 m/s per second.

Acceleration is easy to spot on a speed vs. time graph. Acceleration causes the line to slope up on a speed vs. time graph. If the hill is steeper, the acceleration is greater.

There is zero acceleration at constant speed because the speed does not change.

Speed and acceleration are not the same thing.

You can be moving (non-zero speed) and have no acceleration (think cruise control). You can also be accelerating and not moving!

A falling object begins accelerating the instant it is released.

Acceleration describes how quickly speed changes.

Acceleration is the change in speed divided by the change in time.

Speed and Acceleration

An acceleration of 20 km/h/s means that the speed increases by 20 km/h each second.

The units for time in acceleration are often expressed as “seconds squared” and written as s 2 .

Example: Finding acceleration.

A sailboat moves at 1 m/s. A strong wind increases its speed to 4 m/s in 3 s. Calculate acceleration.

1. Looking for: acceleration of sailboat

2. Given: v1 = 1 m/s; v2 = 4 m/s; time = 3 s

3. Relationships: a = v2 – v1/t

4. Solution: a = (4 m/s – 1 m/s)/ 3 s

= 1 m/s2

Acceleration on Motion Graphs

The word “acceleration” is used for any change in speed, up or down.

Acceleration can be positive or negative.

Acceleration on speed vs. time graphs

Positive acceleration adds more speed each second.

Things get faster.

Speed increases over time.

AND

Negative acceleration subtracts some speed each second.

Things get slower.

People sometimes use the word deceleration to describe slowing down.

Acceleration on Position vs. Time Graphs

The position vs. time graph is a curve when there is acceleration.

The car covers more distance each second, so the position vs. time graph gets steeper each second.

When a car is slowing down, the speed decreases so the car covers less distance each second.

The position vs. time graph gets shallower with time.

Free Fall

An object is in free fall if it is accelerating due to the force of gravity and no other forces are acting on it.

The letter “g” is used for acceleration due to gravity.

Falling objects increase their speed by 9.8 m/s every second, or 9.8 m/s2.

Acceleration and DirectionAcceleration occurs whenever there is a change in speed, direction, or both. A car driving around a curve at a constant speed is accelerating because its direction is changing.

Curved Motion

A soccer ball is an example of a projectile.

A projectile is an object moving under the influence of only gravity.

The path of the ball makes a bowl-shaped curve called a parabola.

Circular motion is another type of curved motion.

An object in circular motion has a velocity vector that constantly changes direction.

Section 3 Vocabularyacceleration – the rate at which velocity changes.

free fall – accelerated motion that happens when an object falls with only the force of gravity acting on it.

acceleration due to gravity – the value of 9.8 m/s2, which is the acceleration in free fall at Earth’s surface, usually represented by the lowercase letter, g.

projectile – an object moving through space and affected only by gravity.

Section 3 Review Questions1. Nearly all physics problems will use the unit m/s2 for acceleration. Explain why the seconds are squared. Why isn't the unit given as m/s as it is for speed?______________________________________________________________________________________________________________________________________________________2. Suppose you are moving left (negative) with a velocity of -10 m/s. What happens to your speed if you have a negative acceleration? Do you speed up or slow down?

______________________________________________________________________________________________________________________________________________________

3. A rabbit starts from a resting position and moves at 6 m/s after 3 seconds. What is the acceleration of the rabbit? ______________________________________________________

4. You are running a race and you speed up from 3 m/s to 5 m/s in 4 seconds.

a. What is your change in speed? ______________________________

b. What is your acceleration? __________________________________

5. Does a car accelerate when it goes around a corner at a constant speed? Explain your answer. _______________________________________________________________________________________________________________________________________________

6. A sailboat increases its speed from 1 m/s to 4 m/s in 3 seconds. What will the speed of the sailboat be at 6 seconds if the acceleration stays the same? __________________________

7. The graph on page 99 of the textbook shows the speed of a person riding a bicycle through a city. Which point (A, B, or C) on the graph is a place where the bicycle has speed but no acceleration? How do you know? ______________________________________________________________________________________________________________________________________________________________________________________________________

8. What happens to the speed of an object what is dropped in free fall? ______________________________________________________________________________________________________________________________________________________

9. A ball is in free fall after being dropped. What will the speed of the ball be after 2 seconds of free fall? ____________________________________________________________________

10. What happens when velocity and acceleration are not in the same direction? What kind of motion occurs? _________________________________________________________________________________________________________________________________________

11. The Earth moves in a nearly perfect circle around the Sun. Assume the speed stays constant. Is the Earth accelerating or not? ____________________________________________________________________________________________________________________

Name:________________________________ Date:____________ Period: _____

Unit 2: Motion, Section 3: AccelerationGuided Acceleration Equation Practice

Acceleration is the rate of change in the speed of an object. To determine the rate of acceleration, you use the formula below. The units for acceleration are meters per second per second or m/s2. A positive value for acceleration shows speeding up, and negative value for acceleration shows slowing down.Slowing down is also called deceleration. Final speed is also written as v2 and beginning speed is also written as v1. Remember that acceleration can be negative.

Acceleration = Final Speed – Beginning Speed Time

Complete each of the acceleration problems and then we will go over them as a class. Please use the format below to complete each problem on a separate sheet of paper.

Example: How fast was a car accelerating if it went from 0 -70 mph in 5 seconds?

Looking forAcceleration of the car.

Solution

Acceleration = 70 mph – 0 mph = 14.0 mph/s 5.0 s

The acceleration of the car is 14 miles per hour per second.

GivenBeginning speed (v1) = 0 mphFinal speed (v2) = 70 mphChange in time = 5.0 secondsRelationship a = v2 - v1 t

1. What is the acceleration of a bicycle traveling at 3 m/s which increases to 10 m/s after 28 seconds?

________________________2. What is the acceleration of a bicycle traveling at 15 m/s which decreases to 5 m/s after 5 seconds?

________________________

3. A cruise ship is leaving port at a speed of 50 meters per minute (m/m). After 10 minutes the ship is clear of the dock and is now traveling at 100 m/m. What was its acceleration?

________________________4. If a cheetah reaches 95 km/hr in 30 seconds, what was its acceleration?

________________________5. A goose approaches a pond in order to land in the water. The goose was flying at a speed of 5 m/s at the beginning of the dissent and 0.5 m/s when it is fully in the water. It took a total of 1 minute to complete its dissent.

________________________6. A ball is dropped from a window and reaches the ground after 4 seconds. What was the ball’s acceleration? What was the ball’s speed at the point of impact with the ground? (Hint: acceleration due to gravity is a constant rate.)

a = ____________________

s = ____________________Name:________________________________ Date:____________ Period: _____

Unit 2: Motion, Section 3: AccelerationAcceleration Problem Practice

Acceleration is the rate of change in the speed of an object. To determine the rate of acceleration, you use the formula below. The units for acceleration are meters per second per second or m/s2. A positive value for acceleration shows speeding up, and negative value for acceleration shows slowing down.Slowing down is also called deceleration.

Acceleration = Final Speed – Beginning Speed Time

Final speed is also written as v2 and beginning speed is also written as v1. The acceleration formula can be rearranged to solve for other variables such as final speed (v2) and time (t).

v2 = v1 + (a x t) and t = v2 – v1a

Example 1. A skater increases her velocity from 2.0 m/s to 10.0 m/s in 3.0 seconds. What is the skater’s acceleration?

Looking forAcceleration of the skater.

Solution

Acceleration = 10.0 m/s – 2.0 m/s = 2.7 m/s2

3.0 s

GivenBeginning speed = 2.0 m/sFinal speed = 10.0 m/sChange in time = 3.0 seconds

The acceleration of the skater is 2.7 meters persecond per second.

Relationship a = v2 - v1 t

Example 2. A car accelerates at a rate of 3.0 m/s2. If its original speed is 8.0 m/s, how many seconds will it take the car to reach a final speed of 25.0 m/s?

Looking forThe time to reach the final speed.

Solution

Time = 25.0 m/s – 8.0 m/s = 5.7 s 3.0 m/s2

The time for the car to reach its final speed is5.7 seconds.

GivenBeginning speed = 8.0 m/sFinal speed = 25.0 m/sAcceleration = 3.0 m/s2Relationship t = v2 – v1

a

1. While traveling along a highway, a driver slows from 24 m/s to 15 m/s in 12 seconds. What is theautomobile’s acceleration? (Remember that a negative value indicates a slowing down or deceleration.) ________________2. A parachute on a racing dragster opens and changes the speed of the car from 85 m/s to 45 m/s in a period of 4.5 seconds. What is the acceleration of the dragster? ________________3. The table below contains data for a ball rolling down a hill. Fill in the missing data values in the table and determine the acceleration of the rolling ball.

Acceleration = ___________

4. A car traveling at a speed of 30.0 m/s encounters an emergency and comes to a complete stop. How much time will it take for the car to stop if it decelerates at –4.0 m/s2? ________________

Time (seconds) Speed (km/h)0 (start) 0 (start)

2 369

810 15

5. If a car can go from 0 to 60 mph in 8.0 seconds, what would be its final speed after 5.0 seconds if its starting speed were 50 mph? ________________6. A cart rolling down an incline for 5.0 seconds has an acceleration of 4.0 m/s2. If the cart has a beginning speed of 2.0 m/s, what is its final speed? ________________7. A helicopter’s speed increases from 25 m/s to 60 m/s in 5 seconds. What is the acceleration of thishelicopter? ________________8. As she climbs a hill, a cyclist slows down from 25 mph to 6 mph in 10 seconds. What is her deceleration? ________________9. A motorcycle traveling at 25 m/s accelerates at a rate of 7.0 m/s2 for 6.0 seconds. What is the final speed of the motorcycle? ________________10. A car starting from rest accelerates at a rate of 8.0 m/s2. What is its final speed at the end of 4.0 seconds? ________________11. After traveling for 6.0 seconds, a runner reaches a speed of 10. m/s. What is the runner’s acceleration? ________________12. A cyclist accelerates at a rate of 7.0 m/s2. How long will it take the cyclist to reach a speed of 18 m/s? ________________13. A skateboarder traveling at 7.0 meters per second rolls to a stop at the top of a ramp in 3.0 seconds. What is the skateboarder’s acceleration? ________________