Acceleration

Acceleration Measures Changes in Velocity

• The quantity that describes the rate of change of velocity in a given time interval is called acceleration.

• The SI units for acceleration are meters per second per second (m/s/s or m/s2)

Acceleration

• avg acceleration = (change in velocity)/(change in time)

• aavg = Δv/Δt = (vf-vi)/tf-ti)

Acceleration Practice

• As a shuttle bus comes to a normal stop, it slows from 9m/s to 0m/s in 5s. Find the average acceleration of the bus.

Acceleration

• #s 1-5 on pg. 49

Acceleration has Direction and Magnitude

• Positive acceleration is when the change in velocity is positive (speeding up).

• Negative acceleration is when the change in velocity is negative (slowing down or the direction of the object is moving backwards).

Velocity vs. Time Graph

• The slope of a velocity vs. time graph gives you the acceleration.

Velocity vs. Time Graph

Displacement due to Acceleration

• Displacement depends on Acceleration, Initial Velocity, and Time

• Displacement with constant acceleration:• Δx = ½(vi+vf)Δt

Displacement with Constant Acceleration

• A racing car reaches a speed of 42m/s. It then begins a uniform negative acceleration, using its parachute and braking system, and comes to rest 5.5s later. Find how far the car moves while stopping.

Displacement with Constant Acceleration

• #s 1-5 on pg. 53

Final Velocity due to Acceleration

• Velocity with constant acceleration:• vf = vi + aΔt

Displacement with Constant Acceleration

• Δx = viΔt + ½a(Δt)2

• This equation is useful for finding how far an object travels under constant acceleration AND for finding the distance required for an object to reach a certain speed or to come to a stop.

Velocity and Displacement with Constant Acceleration

• A plane starting at rest at one end of a runway undergoes a constant acceleration of 4.8m/s2 for 15s before takeoff. What is its speed at take off? How long must the runway be for the plane to be able to take off?

Velocity and Displacement with Constant Acceleration

• #s 1-4 on pg 55

Final Velocity after any Displacement

• vf2=vi

2 + 2aΔx

• A baby sitter pushing a stroller starts from rest and accelerates at a rate of 0.50m/s/s. What is the velocity of the stroller after it has traveled 4.75m?

Final Velocity after any Displacement

• #s 1-5 on pg 58

Falling Objects

Free Falling Bodies

• Freely falling bodies undergo constant acceleration

• Free fall is where objects dropped near the surface of a planet fall with the same constant acceleration in the absence of air resistance.

Free Fall

• Velocity is increasing by the same amount in each time interval which causes a constant acceleration.

Free Fall• Free fall acceleration is represented by the

symbol g.

• At the surface of Earth the magnitude of g is 9.81 m/s/s.

• Since this acceleration is directed downward towards the earth, it will have a negative assigned to it -9.8m/s/s

Free Fall

• Jason hits a volleyball so that it moves with an initial velocity of 6m/s straight upward. If the volleyball starts from 2m above the floor, how long will it be in the air before it strikes the floor?

Free Fall

• #s 1-6 on pg 64