Kinematics II Acceleration
Acceleration is the rate of change of velocity with respect to time If you are in a car that is speeding up or slowing down, you and the car are accelerating If you make a turn at constant speed, you are accelerating, too (Why?)
𝒂 𝒂𝒗𝒈 = ∆𝒗 ∆𝒕 = 𝒗 𝒇 − 𝒗 𝒊 𝒕 𝒇 − 𝒕 𝒊 Average Acceleration 𝒂 𝒂𝒗𝒈 = ∆𝒗 ∆𝒕 = 𝒗 𝒇 − 𝒗 𝒊 𝒕 𝒇 − 𝒕 𝒊 change in velocity average acceleration = time required for change
Example: A car speeds up from 7.0 m/s to 25.0 m/s in 4.5 s. What is the average acceleration? x t = 0 t = 4.5 s vi = 7.0 m/s vf = 25 m/s 𝑎 𝑎𝑣𝑔 = 𝑣 𝑓 − 𝑣 𝑖 𝑡 𝑓 − 𝑡 𝑖 = 25.0𝑚/𝑠−7.0𝑚/𝑠 4.5𝑠 = 18.0𝑚/𝑠 4.5𝑠 =4.0 𝑚/ 𝑠 2
Position-Time Graphs Show an object’s position as a function of time. x-axis: time y-axis: position
1 2 3 4 5 6 7 8 9 10 position (cm) time (s)
What are the characteristics of this graph? Straight line, upward slope What kind of motion created this graph? Constant speed 1 2 3 4 5 6 7 8 9 10 time (s) position (cm)
Constant speed is represented by a straight segment on the P-T graph. time (s) pos. (m) Constant speed in positive direction. time (s) pos. (m) Constant speed in negative direction.
Constant speed is represented by a straight segment on the P-T graph. time (s) pos. (m) A horizontal segment means the object is at rest.
Curved segments on the P-T graph mean the object’s speed is changing. time (s) pos. (m) Speeding up in positive direction. time (s) pos. (m) Speeding up in negative direction.
Curved segments on the P-T graph mean the object’s speed is changing. time (s) pos. (m) Traveling in positive direction, but slowing down. time (s) pos. (m) Traveling in negative direction, but slowing down.
The slope of a P-T graph is equal to the object’s velocity in that segment. change in y change in x time (s) position (m) 10 20 30 40 50 slope = (30 m – 10 m) (30 s – 0 s) slope = (20 m) (30 s) slope = 0.67 m/s
The following P-T graph corresponds to an object moving back and forth along a straight path. Can you describe its movement based on the graph? time (s) position (m) N S