Opening Activity Compare and contrast the following: Speed and velocity Distance and displacement Average speed and instantaneous speed A cyclist must travel 800 km. How many days will the trip take if the cyclist travels 8 h/day at an average speed of 16 km/h?

3.2 Acceleration pp 76-80 Essential Questions How are time, velocity, and acceleration related? How do I calculate the average acceleration of an object? What is positive and negative acceleration and how are they different?

Acceleration, Speed, and Velocity p 76 When a car takes from a stop, the car’s velocity increases. It also accelerates. Acceleration is the change in velocity divided by the time for the change to occur

Acceleration, Speed, and Velocity p 76 When a car slows down and stops, the car’s velocity decreases. It also accelerates (deceleration).

Changing Direction p 77 Acceleration occurs when an object changes its speed, its direction, or both. We now have three terms that have magnitude (size) and direction; these are vectors. Name the other two vectors we have covered

Changing Direction p 77 Any time a moving object changes direction, its velocity changes and it is accelerating.

Calculating Acceleration 𝒂= Δ𝒗 Δ𝒕 = 𝒗𝒇 − 𝒗𝒊 𝒕𝒇 − 𝒕𝒊 Standard units = m/s2 If a = 1 m/s2, it means that its velocity (speed) is increasing 1 m/s every second.

Suppose a jet airliner starts at rest at the end of a runway and reaches a speed of 80 m/s in 20 s. What is the plane’s average acceleration?

Suppose a jet airliner starts at rest at the end of a runway and reaches a speed of 80 m/s in 20 s. What is the plane’s average acceleration? vi = _____ vf = ______ Δt = _____

Suppose a jet airliner starts at rest at the end of a runway and reaches a speed of 80 m/s in 20 s. What is the plane’s average acceleration? vi = 0 m/s vf = ______ Δt = _____

Suppose a jet airliner starts at rest at the end of a runway and reaches a speed of 80 m/s in 20 s. What is the plane’s average acceleration? vi = 0 m/s vf = 80 m/s Δt = _____

Suppose a jet airliner starts at rest at the end of a runway and reaches a speed of 80 m/s in 20 s. What is the plane’s average acceleration? vi = 0 m/s vf = 80 m/s Δt = 20 s

Suppose a jet airliner starts at rest at the end of a runway and reaches a speed of 80 m/s in 20 s. What is the plane’s average acceleration? vi = 0 m/s vf = 80 m/s Δt = 20 s 𝒂= Δ𝒗 Δ𝒕

Suppose a jet airliner starts at rest at the end of a runway and reaches a speed of 80 m/s in 20 s. What is the plane’s average acceleration? vi = 0 m/s vf = 80 m/s Δt = 20 s 𝒂= Δ𝒗 Δ𝒕 = 𝒗𝒇 − 𝒗𝒊 𝒕𝒇 − 𝒕𝒊

Suppose a jet airliner starts at rest at the end of a runway and reaches a speed of 80 m/s in 20 s. What is the plane’s average acceleration? vi = 0 m/s vf = 80 m/s Δt = 20 s 𝒂= Δ𝒗 Δ𝒕 = 𝒗𝒇 − 𝒗𝒊 𝒕𝒇 − 𝒕𝒊 = 𝟖𝟎 𝒎 𝒔 − 𝟎 𝒎 𝒔 𝟐𝟎 𝒔

Suppose a jet airliner starts at rest at the end of a runway and reaches a speed of 80 m/s in 20 s. What is the plane’s average acceleration? vi = 0 m/s vf = 80 m/s Δt = 20 s 𝒂= Δ𝒗 Δ𝒕 = 𝒗𝒇 − 𝒗𝒊 𝒕𝒇 − 𝒕𝒊 = 𝟖𝟎 𝒎 𝒔 − 𝟎 𝒎 𝒔 𝟐𝟎 𝒔 = 𝟒𝟎 𝒎/𝒔 𝟐𝟎 𝒔

Suppose a jet airliner starts at rest at the end of a runway and reaches a speed of 80 m/s in 20 s. What is the plane’s average acceleration? vi = 0 m/s vf = 80 m/s Δt = 20 s 𝒂= Δ𝒗 Δ𝒕 = 𝒗𝒇 − 𝒗𝒊 𝒕𝒇 − 𝒕𝒊 = 𝟖𝟎 𝒎 𝒔 − 𝟎 𝒎 𝒔 𝟐𝟎 𝒔 = 𝟒𝟎 𝒎/𝒔 𝟐𝟎 𝒔 = 2.0 m/s2

Now imagine that a skateboarder is moving in a straight line at a constant speed of 3 m/s and comes to a stop in 2 seconds. What is the skateboard’s average acceleration?

Now imagine that a skateboarder is moving in a straight line at a constant speed of 3 m/s and comes to a stop in 2 seconds. What is the skateboard’s average acceleration? vi = _____ vf = _____ Δt = _____

Now imagine that a skateboarder is moving in a straight line at a constant speed of 3 m/s and comes to a stop in 2 seconds. What is the skateboard’s average acceleration? vi = 3 m/s vf = 0 m/s Δt = 2 s

Now imagine that a skateboarder is moving in a straight line at a constant speed of 3 m/s and comes to a stop in 2 seconds. What is the skateboard’s average acceleration? vi = 3 m/s vf = 0 m/s Δt = 2 s 𝒂= Δ𝒗 Δ𝒕 = 𝒗𝒇 − 𝒗𝒊 𝒕𝒇 − 𝒕𝒊

Now imagine that a skateboarder is moving in a straight line at a constant speed of 3 m/s and comes to a stop in 2 seconds. What is the skateboard’s average acceleration? vi = 3 m/s vf = 0 m/s Δt = 2 s 𝒂= Δ𝒗 Δ𝒕 = 𝒗𝒇 − 𝒗𝒊 𝒕𝒇 − 𝒕𝒊 = 𝟎 𝒎 𝒔 − 𝟑 𝒎 𝒔 𝟐 𝒔

Now imagine that a skateboarder is moving in a straight line at a constant speed of 3 m/s and comes to a stop in 2 seconds. What is the skateboard’s average acceleration? vi = 3 m/s vf = 0 m/s Δt = 2 s 𝒂= Δ𝒗 Δ𝒕 = 𝒗𝒇 − 𝒗𝒊 𝒕𝒇 − 𝒕𝒊 = 𝟎 𝒎 𝒔 − 𝟑 𝒎 𝒔 𝟐 𝒔 = −𝟑 𝒎/𝒔 𝟐 𝒔 = -1.5 m/s2

Opening Activity It takes a car one minute (60 seconds) to go from a dead stop to a speed of 40 m/s. What is the average acceleration of the car? A truck cruising at 50 m/s slams on its brakes to avoid a collision, stopping in 3.5 s. What is the acceleration of the truck

Opening Activity It takes a car one minute (60 seconds) to go from a dead stop to a speed of 40 m/s. What is the average acceleration of the car?

Opening Activity It takes a car one minute (60 seconds) to go from a dead stop to a speed of 40 m/s. What is the average acceleration of the car? t = 60s vi = 0 m/s vf = 40 m/s a = ???

Opening Activity It takes a car one minute (60 seconds) to go from a dead stop to a speed of 40 m/s. What is the average acceleration of the car? t = 60s vi = 0 m/s vf = 40 m/s a = ??? = (vf – vi)/(tf – ti)=(40-0)/60 = 0.67 m/s2

Opening Activity A truck cruising at 50 m/s slams on its brakes to avoid a collision, stopping in 3.5 s. What is the acceleration of the truck?

Opening Activity A truck cruising at 50 m/s slams on its brakes to avoid a collision, stopping in 3.5 s. What is the acceleration of the truck? t = 3.5s vi = 50 m/s vf = 0 m/s a = ???

Opening Activity A truck cruising at 50 m/s slams on its brakes to avoid a collision, stopping in 3.5 s. What is the acceleration of the truck? t = 3.5s vi = 50 m/s vf = 0 m/s a = ??? = (vf – vi)/(tf – ti)=(0-50)/3.5 = -14.29 m/s2

Speed-Time Graphs – Calculating Positive Acceleration 𝒂= Δ𝒗 Δ𝒕 = 𝒗𝒇 − 𝒗𝒊 𝒕𝒇 − 𝒕𝒊 = 𝟖𝟎 𝒎 𝒔 − 𝟎 𝒎 𝒔 𝟐𝟎 𝒔 = 𝟒𝟎 𝒎/𝒔 𝟐𝟎 𝒔 = 2.0 m/s2

Speed-Time Graphs – Calculating Negative Acceleration 𝒂= Δ𝒗 Δ𝒕 = 𝒗𝒇 − 𝒗𝒊 𝒕𝒇 − 𝒕𝒊 = 𝟎 𝒎 𝒔 − 𝟑 𝒎 𝒔 𝟐 𝒔 = −𝟑 𝒎/𝒔 𝟐 𝒔 = -1.5 m/s2

3.2 Homework p 80 1-7 (All classes) p 880 26-28, 30-32 (Honors)