Acceleration and Free Fall Chapter 2.2 and 2.3

What is acceleration? Acceleration measures the rate of change in velocity. Average acceleration = change in velocity/ time required for change

Units for acceleration

Sign is very important! Acceleration has both direction and magnitude A negative value for acceleration does not always mean an object is decelerating!!

Speeding up, moving to the left Slowing down, moving to the rightSpeeding up, moving to the right 2-4 Acceleration Increasing speed and deceleration (decreasing speed) should not be confused with the directions of velocity and acceleration: Slowing down, moving to the left

Fill in the Chart Initial VelocityAccelerationMotion ++ Speeding up, moving right/up -- Speeding up, moving left/down +- Slowing Down moving right/up -+ Slowing Down, moving left/down - or +0 Constant Velocity 0- or + Speeding up from rest 00 Remaining at rest

Graph of Velocity vs Time Question: What does the slope of this graph give you? Rise = Δv Run Δt Answer: ACCELERATION V f – V AVG = Δv t f – t i = Δt

The Kinematic Equations You are going to loooooove these!

Motion with constant acceleration Kinematic Equations The relationships between displacement, velocity and constant acceleration are expressed by equations that apply to any object moving with constant acceleration.

Displacement with constant acceleration Δx = displacement V i = initial velocity V f = final velocity Δt = time interval

Example: #1 p.53 in book A car accelerates uniformly from rest to a speed of 23.7 km/h in 6.5 s. Find the distance the car travels during this time. Δx = displacement= distance= ? V i = initial velocity = rest = 0 km/h V f = final velocity = 23.7 km/h Δt = time interval = 6.5 s Look at final velocity…convert to m/s!!!

Problem Solving Final velocity conversion Plug in values and solve for Δx

Velocity with constant uniform acceleration V f = final velocity V i = initial velocity a = acceleration Δt = time interval

Example: #2 p.55 An automobile with an initial speed of 4.30 m/s accelerates uniformly at the rate of 3.0 m/s 2. Find the final speed after 5.0 seconds. V f = final velocity=? V i = initial velocity = 4.3 m/s a = acceleration= 3.0 m/s^2 Δt = time interval= 5.0 s

Solve Plug in values and solve for Vf V f = 19 m/s

Displacement with constant uniform acceleration Δx = displacement V i = initial velocity a = acceleration Δt = time interval

Example: #2 p.55 An automobile with an initial speed of 4.30 m/s accelerates uniformly at the rate of 3.0 m/s 2. Find the displacement after 5.0 seconds. Δx = displacement=?? Vi = initial velocity= 4.30 m/s a = acceleration= 3.0 m/s^2 Δt = time interval= 5.0 s

Solve! Plug in values and solve for displacement

Final Velocity after any displacement V f = final velocity V i = initial velocity a = acceleration Δx = displacement

Example: p.58 #3 A car accelerates uniformly in a straight line from rest at the rate of 2.3 m/s^2. What is the speed of the car after it has traveled 55 m? Vf = final velocity=?? Vi = initial velocity= rest= 0 m/s a = acceleration= 2.3 m/s^2 Δx = displacement= 55 m

Solve

Rearranging Your problems won’t always be so straightforward…make sure to rearrange your equations to solve for the unknown before plugging in your numbers (with units!)

Section 2-3 Falling Objects Free Fall: Neglecting air resistance, all objects fall with the same constant acceleration

Acceleration due to gravity

Free Fall Acceleration However, acceleration is a vector. Gravity acts toward the earth (down) Therefore, the acceleration of objects in free fall near the surface of the earth is

What we see because of air resistance…

Object falling from rest

Path of a projectile At top of path v= 0 m/s a = m/s 2

Free Fall Acceleration At the highest point of an arc, an object has velocity = 0 m/s, acceleration is still m/s 2 An object thrown into the air is a freely falling body with

Free Fall Problem p.64 #2 A flowerpot falls from a windowsill 25.0 m above the sidewalk A. How fast is the flowerpot moving when it strikes the ground? B. How much time does a paserby on the sidewalk below have to move out of the way before the flowerpot hits the ground?

Part. A. What are we looking for: V f What do we know? Displacement: -25 m Acceleration: m/s 2 V i =0 m/s What equation should we use??

Solve the problem

Part b. How much time before the flowerpot hits the ground? What do we know? Displacement= m Acceleration = m/s 2 V initial= 0 V final = m/s What are we looking for: Time! Which equation should we use??

Solve the Problem