Average Velocity

change in position

change in time

P

t

∆ =∆

Average Acceleration

change in velocity

change in time

V

t

∆ =∆

Velocity at a specific time?

•Ins tantaneous Derivative of pos ition and plug in the time

• Units : m/s , ft/s , etc .

Acceleration at a specific time?

•Ins tantaneous Derivative of velocity (s econd derivative of pos ition) and plug in the time

• Units : m/s 2, ft/s 2, etc .

How long has an object been in the air?

•Looking for t and talking about position

•Set s(t) or position = 0, solve for t (this finds when the object was on the ground)

•If you know when the object is on the ground you can determine how long it is in the air!

Initial Pos ition or Velocity or Acceleration

•Initial = from the S TART! S o t=0

•Plug in 0 in for the appropriate equation

Maximum Height?(for projectile motion/object

projected into the air)

•Velocity = 0 at the max height (s lope of the tangent line is 0, s lope goes from + to – or – to +)

•S o find t by setting velocity equal to 0 and then plug in t into pos ition to determine the height

When is the object at res t?

•S ame as max height time (velocity is 0, no movement)

•Velocity = 0, solve for t

What is the velocity when the object hits the ground

( impact velocity)?

•Looking for v(t), but you need a time first (time when the object hits the ground)

•Set s(t) or position = 0, solve for t (this finds when the object was on the ground)

•Now plug in t into v(t)

Displacement

•Final Pos ition – Initial Pos ition(make sure to indicate direction, left/right, etc .)

S peed

• |v(t) |

• magnitude of velocity

Total Dis tance

•Determine the starting and ending positions

•Find when the object changes direction (v(t)=0 and solve for t)

•Then find the distance traveled for each section and add them together