Acceleration Physics Mr Berman Part I n n

Acceleration Physics Mr. Berman

Part I n n Average Acceleration Instantaneous Acceleration Deceleration Uniform Accelerated Motion

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

Simulation of Constant Velocity Compared to Constant Acceleration n http: //higheredbcs. wiley. com/legacy/college/h alliday/0471320005/simulations 6 e/index. htm ? newwindow=true

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

Note: n Dv = final velocity – initial velocity

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

Instantaneous Acceleration n Instantaneous Acceleration is the acceleration at a given instant. n 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 2 m/s are you accelerating? 2. When you are riding in a car at a constant speed of 5 mph turning right, are you accelerating?

Signs of Acceleration n Acceleration is + when Dv > 0 n Acceleration is when Dv < 0 -

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

Uniform Accelerated Motion n Motion with constant acceleration q Straight line q 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. 5 m/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. 5 m/s 2

Example 2 n The bee decides to slow down from +1. 75 m/s to +0. 75 m/s in 2 s. 1. 3. Draw the motion diagram. Draw the vector diagram. What was the acceleration of the bee? n Answer: -0. 5 m/s 2 2.

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

Example 3: n Susan slides on the icy sidewalk with an initial velocity of 2 m/s. She slows down for 3 s at 0. 5 m/s 2. Draw the vector diagram. What is her final velocity? n Answer: 0. 5 m/s n n

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

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

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

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

n The slope of the line of the velocity- time graph is the instantaneous acceleration. n For constant acceleration that slope also equals the average acceleration. n 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 Acceleration (m/s 2) + o Positive Acceleration Time (s)

Give a qualitative example of the previous motion.

Example 2: Position vs Time Position (m) + Parabola o Time (s) 1. What is the slope of the tangent to the curve at t=5 s? 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? 5 s

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

Acceleration vs Time Acceleration (m/s 2) + o Time (s) • 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 v(m/s) 10 m/s 5 m/s o 10 s Time (s) • Hint: Area Under the Line=Displacement Δd or simply d Answer: 75 m