Acceleration Physics Mrs. Coyle

Part I Average Acceleration Instantaneous Acceleration Deceleration Uniform Accelerated Motion

Acceleration The rate of change of velocity per unit time. It is a vector quantity.

Simulation of Constant Velocity Compared to Constant Acceleration alliday/ /simulations6e/index.htm? newwindow=true alliday/ /simulations6e/index.htm? newwindow=true

Average Acceleration = Change in Velocity Time Interval a =  v  t a = v 2 - v 1 t 2 – t 1 Average Acceleration

Note:  v = final velocity – initial velocity

Units of Acceleration Examples of units of acceleration are: m/s 2 or m/s/s km/h 2 or km/h/h km/h/s

Instantaneous Acceleration Instantaneous Acceleration is the acceleration at a given instant. Can you always tell if you are accelerating while observing the speedometer of a car?

Questions: 1. If you are riding on a merry-go-round at a constant speed of 2m/s are you accelerating? 2. When you are riding in a car at a constant speed of 5mph turning right, are you accelerating?

Signs of Acceleration Acceleration is + when  v > 0 Acceleration is - when  v < 0

Deceleration Deceleration is acceleration that causes the velocity’s magnitude to be reduced. Is it necessary for deceleration to be negative?

Uniform Accelerated Motion Motion with constant acceleration  Straight line  Same direction

Example 1: “The Bee” A bee is flying in the air with an initial velocity of +0.5 m/s. It then accelerates for 2.0 s to a velocity of +1.5m/s. 1. Draw a motion diagram. 2. Draw a vector diagram showing the initial and final velocity and the acceleration of the bee. 3. Calculate the acceleration of the bee. Answer: +0.5m/s 2

Example 2 The bee decides to slow down from +1.75m/s to +0.75m/s in 2s. 1. Draw the motion diagram. 2. Draw the vector diagram. 3. What was the acceleration of the bee? Answer: -0.5m/s 2

Solving for v f : v f = v i + a Δt v f = v i + a t

Example 3: Susan slides on the icy sidewalk with an initial velocity of 2m/s. She slows down for 3s at 0.5m/s 2. Draw the vector diagram. What is her final velocity? Answer: 0.5m/s

Part II Graphs of Accelerated Motion Position-Time Velocity-Time Acceleration-Time

Example 1: Position vs Time Time (s) o Position (m) Parabola 1.What is the slope of the tangent to the curve at t=0s? 2.Is the slope of the tangent to the curve increasing or decreasing with increasing time? +

Note: The slope of the tangent to the curve at a given time of the position-time graph is the instantaneous velocity.

Velocity vs Time Time (s) o Velocity (m/s) Slope of Line= Acceleration Area Under Line=Displacement (Change in Position) +

The slope of the line of the velocity- time graph is the instantaneous acceleration. For constant acceleration that slope also equals the average acceleration. For motion with varying acceleration, the velocity graph would be a curve. The slope of the tangent to the curve at a given time would represent the instantaneous acceleration.

Acceleration vs Time Time (s) o Acceleration (m/s 2 ) Positive Acceleration +

Give a qualitative example of the previous motion.

Example 2: Position vs Time Time (s) 5s o Position (m) Parabola 1.What is the slope of the tangent to the curve at t=5s? 2.Is the slope to the tangent, positive or negative at t=0 s? 3.Is the slope of the tangent, increasing or decreasing with increasing time? +

Velocity vs Time Time (s) o Velocity (m/s) Is the slope of the line positive or negative? +

Acceleration vs Time Time (s) o Acceleration (m/s 2 ) The acceleration is negative. +

Give a qualitative example of the previous motion?

Note: Area Under Line of the velocity-time graph =Displacement (Change in Position) Area under the line of the acceleration-time graph =Change in Velocity

Example: Calculate the displacement between 0 and 10 s Time (s) o v(m/s) Hint: Area Under the Line=Displacement Δd or simply d 10m/s 5m/s 10s Answer: 75m