Dr. Joseph W. Howard ©Summer 2006 Motion Scenarios EastWest 0 s 0 m 1 s 1 m 8 s 8 m 7 s 7 m 6 s 6 m 5 s 5 m 4 s 4 m 3 s 3 m 2 s 2 m Each vector is exactly the same direction and length Each vector is exactly the same direction and length Each second of time covers the same distance Each second of time covers the same distance “Constant Velocity” “Constant Velocity” The vector arrows represent velocity. A velocity vector is an arrow whose length represents the speed of an object in motion and the direction of that motion. The vector arrows represent velocity. A velocity vector is an arrow whose length represents the speed of an object in motion and the direction of that motion.

Dr. Joseph W. Howard ©Summer 2006 Motion Scenarios EastWest 0 s 0 m 1 s 1 m8 m7 m6 m 5 s 5 m 4 s 4 m 3 s 3 m 2 s 2 m “Speeding UP” “Speeding UP” Each velocity vector is getting longer than the previous one but still in same direction. Each velocity vector is getting longer than the previous one but still in same direction. Each second of time covers a larger distance Each second of time covers a larger distance This is showing a “ change ” in velocity! This is showing a “ change ” in velocity!

Dr. Joseph W. Howard ©Summer 2006 Motion Scenarios EastWest 0 s 0 m 1 s 1 m8 m7 m6 m 5 s 5 m 4 s 4 m 3 s 3 m 2 s 2 m “Slowing Down” “Slowing Down” Each velocity vector is getting shorter than the previous one but still in same direction. Each velocity vector is getting shorter than the previous one but still in same direction. Each second of time covers a smaller distance Each second of time covers a smaller distance This is showing a “ change ” in velocity! This is showing a “ change ” in velocity!

Dr. Joseph W. Howard ©Summer 2006 Acceleration Acceleration = (Change in Velocity) (Time Taken During Change) Note that because acceleration depends upon a change in velocity, it’s possible for there to be a non-zero acceleration without changing speed, e.g., when a car goes around a curve at constant speed, it’s direction is changing, so you feel an acceleration. This is why you feel pushed towards one side or the other of the car. Note that because acceleration depends upon a change in velocity, it’s possible for there to be a non-zero acceleration without changing speed, e.g., when a car goes around a curve at constant speed, it’s direction is changing, so you feel an acceleration. This is why you feel pushed towards one side or the other of the car. Whenever the velocity vector changes we say there was acceleration. Whenever the velocity vector changes we say there was acceleration. Units:

Dr. Joseph W. Howard ©Summer 2006 Motion Scenarios w/ Acceleration EastWest 0 s 0 m 1 s 1 m 8 s 8 m 7 s 7 m 6 s 6 m 5 s 5 m 4 s 4 m 3 s 3 m 2 s 2 m “Constant Velocity” “Constant Velocity” No change in velocity No acceleration No change in velocity No acceleration

Dr. Joseph W. Howard ©Summer 2006 EastWest 0 s 0 m 1 s 1 m8 m7 m6 m 5 s 5 m 4 s 4 m 3 s 3 m 2 s 2 m “Speeding UP” “Speeding UP” Motion Scenarios w/ Acceleration Each velocity vector gets longer by this amount each second. This is the ACCELERATION When the acceleration vector and velocity vector are in the same direction the object is “speeding up!” Each velocity vector gets longer by this amount each second. This is the ACCELERATION When the acceleration vector and velocity vector are in the same direction the object is “speeding up!”

Dr. Joseph W. Howard ©Summer 2006 Motion Scenarios EastWest 0 s 0 m 1 s 1 m8 m7 m6 m 5 s 5 m 4 s 4 m 3 s 3 m 2 s 2 m “Slowing Down” “Slowing Down” Each velocity vector gets shorter by this amount each second. This is the ACCELERATION When the acceleration vector and velocity vector are in the opposite directions the object is “slowing down!” Each velocity vector gets shorter by this amount each second. This is the ACCELERATION When the acceleration vector and velocity vector are in the opposite directions the object is “slowing down!”

Dr. Joseph W. Howard ©Summer 2006 Acceleration is a Vector Velocity Before Velocity After Direction of Acceleration

Dr. Joseph W. Howard ©Summer 2006 Example A cat sitting calmly at rest begins to run towards the East accelerating in that direction at a rate of 2 m/s 2. Draw a vector picture to show the cat at 0s, 1s, 2s, 3s, 4s, etc… A cat sitting calmly at rest begins to run towards the East accelerating in that direction at a rate of 2 m/s 2. Draw a vector picture to show the cat at 0s, 1s, 2s, 3s, 4s, etc… East West 0 s 1 s2 s3 s 4 s 5 s 2 m/s 2 m/s 2 4 m/s 2 m/s 2 6 m/s 2 m/s 2 8 m/s

Dr. Joseph W. Howard ©Summer 2006 Example A dog running with a speed of 10 m/s to the west has an acceleration of 2.0 m/s 2 while slowing down. Draw a vector picture to show the dog at 0s, 1s, 2s, 3s, 4s, etc… A dog running with a speed of 10 m/s to the west has an acceleration of 2.0 m/s 2 while slowing down. Draw a vector picture to show the dog at 0s, 1s, 2s, 3s, 4s, etc… East West 0 s1 s2 s3 s4 s5 s 4 m/s 2 m/s 2 6 m/s 2 m/s 2 8 m/s 2 m/s 2 10 m/s 2 m/s 2 2 m/s