Chapter 2 Section 2: Acceleration

Chapter 2 Section 2: Acceleration

Motion Review Speed is the rate that an object s distance changes Distance is how far an object has travelled Speed = distance/time Velocity is rate that an object s displacement changes Displacement is how far the object is from the starting point Velocity = displacement/time When an object travels in only one direction, it s distance and displacement are the same! This means that the value of speed and velocity would also be the same. From this point on, we will assume that objects are moving in one direction away from a starting point and therefore we will refer to velocity as a speed with a direction to stay consistent with your book.

Speed (m/s) Speed vs. Time Graphs What would a speed vs. time graph look like for: An object with a constant speed? An object speeding up? An object slowing down? Time (s) What is the object s speed at this point? 0 m/s

Acceleration Acceleration is the rate of change of velocity When the velocity of an object changes, we call that acceleration Because we are calling velocity a speed with direction, acceleration occurs when there is a change in how fast an object is moving (speeding up or slowing down), the direction in which it is moving, or both

Positive Acceleration Positive acceleration occurs when an object is speeding up Acceleration is in the same direction as the velocity

Negative Acceleration Negative acceleration occurs when an object is slowing down Acceleration is in the opposite direction of velocity We do not call negative acceleration deceleration!

Changing Direction Any time an object changes direction, it s velocity changes even if it is travelling at a constant speed This also means that acceleration changes when an object changes direction even if it is travelling at a constant speed

Speed (m/s) Speed (m/s) Speed (m/s) Graphing Acceleration Because acceleration is a change in velocity over time, we can use speed vs. time graphs to determine if acceleration is positive or negative or if there is no acceleration happening Based on what you know about acceleration, which graph(s) illustrate positive and negative acceleration? Negative Acceleration No Acceleration Positive Acceleration Time (s) Time (s) Time (s)

Calculating Acceleration Acceleration is a change in velocity over time. acceleration (m/s 2 ) = velocity (m s ) or time (s) acceleration (a) = Final velocity v f Initial velocity v i time (t) a = v f vi t or m/s/s or v f vi a t

Acceleration Practice For each problem: List the givens List the formula you will use Write the givens in your formula, including units Show all math calculations List appropriate units on your final answer 1. If a race car goes from 0 to 50 m/s in 5 seconds, what is its acceleration? v i = 0 m/s v f = 50 m/s t = 5 s a =? a = v f vi t a = 50m s 0m s 5 s a = 50m s 5 s a = 10 m/s 2

More Acceleration Practice For each problem: List the givens List the formula you will use Write the givens in your formula, including units Show all math calculations List appropriate units on your final answer 2. If a car travels at 26 m/s and hits the brakes for 4 seconds to come to a complete stop, what is its acceleration? v i = 100 m/s v f = 0 m/s t = 2 s a =? a = v f vi t a = 0m s 26m s 4 s a = 26m s 4 s a = - 6.5 m/s 2

More Acceleration Practice For each problem: List the givens List the formula you will use Write the givens in your formula, including units Show all math calculations List appropriate units on your final answer 3. If a person can accelerate from rest at 2 m/s 2, how fast will he be running after 2 seconds? v i = 0 m/s v f =? t = 5 s a = 2 m/s 2 v f vi = a x t v f 0 m/s = 2 m/s 2 x 2 s v f = 4 m/s

More Acceleration Practice For each problem: List the givens List the formula you will use Write the givens in your formula, including units Show all math calculations List appropriate units on your final answer 4. How long would it take a race car to go from 0 m/s to 45 m/s if it can accelerate at 6 m/s 2? v i = 0 m/s v f = 45 m/s t =? a = 6 m/s 2 t = v f vi a t = 45m s 0m s 6 m/s 2 t = 45m s 6 m/s 2 t = 7.5 s

More Acceleration Practice For each problem: List the givens List the formula you will use Write the givens in your formula, including units Show all math calculations List appropriate units on your final answer 5. If a skier is going downhill with an acceleration of 3 m/s 2 and has a velocity of 18 m/s after 3 seconds, what was her initial velocity? v i =? v f = 18 m/s t = 3 s a = 3 m/s 2 v f vi = a x t 18 m/s v i = 3 m/s 2 x 3 s 18 m/s v i = 9 m/s v i = - 9 m/s v i = 9 m/s