Notes: 11.3 Acceleration

Acceleration A. The rate at which velocity changes. * Recall - Velocity is a combination of speed and direction. The unit for velocity is meters per second. B. Acceleration can be described as changes in speed, direction, or both. Just like velocity!

Ex.) The acceleration of a carousel. *The speed of the carousel is not changing however, you are accelerating. The carousel is constantly going in circles. This is causing a continuous change in direction. Which is a causing a continuous change in acceleration.

Ex.) The acceleration of a roller coaster. *The roller coaster is constantly speeding up, slowing down, and changing direction. This is a constant change in velocity. Not just direction like the carousel. Since the velocity is constantly changing, then so is the acceleration.

Ex.) A plane taking off. *This is an example of constant acceleration (a steady change in velocity) . The plane is taking off in a straight line, but its velocity is changing by the same amount each second.

Acceleration C. The unit for acceleration is meters per second per second or m/s^2. D. Acceleration can be caused by a positive change in speed, a negative change in speed (deceleration), or a change in direction.

Free Fall E. Free fall is the movement of an object toward Earth due to gravity. A. Objects falling near Earth’s surface accelerate downward at a rate of 9.8m/s^2. B. This means that every second an object is in free fall it accelerates at 9.8 meters per second.

Ex. 1) A rock falling of the top of the top of a cliff. *How much time passes between each image of the falling rock? *How does the distance traveled change between successive time intervals? *How does the average speed change between successive time intervals?

Ex. 2) A person bouncing a basketball. *As the ball falls from the person’s hand, how does its speed change? *What happens to the speed of the ball as the ball rises from the floor to the person’s hand? *At what point does the ball have zero velocity? *How does the velocity of the ball change when it bounces on the floor?

Calculating Acceleration A. You can calculate acceleration for a straight line motion by dividing the change in velocity by the total time. B. If “a” is acceleration, vi is the initial velocity, vf is the final velocity, and t is total time then the equation for acceleration can be written as: acceleration = change in velocity/ total time A = (vf - vi) / t

Calculating Acceleration C. In this equation velocity is in the numerator and time is in the denominator. D. If the velocity increases, the numerator is positive and thus the acceleration is also positive. Ex. If you are coasting downhill on a bicycle then your velocity increases and your acceleration is positive.

Now lets do some calculations!!! Yeah!!! Acceleration E. If the velocity decreases, then the numerator is negative and the acceleration is also negative. Ex. If you continue coasting after you reach the bottom of the hill, your velocity decreases and your acceleration is negative. Now lets do some calculations!!! Yeah!!!

A(1) = A(2) = A(3) = Conclusion: Ex.1) Recall the stone falling off of the cliff. Lets calculate the acceleration for each time interval. A(1) = A(2) = A(3) = Conclusion:

Ex. 2) A ball rolls down a ramp, starting from rest Ex. 2) A ball rolls down a ramp, starting from rest. After 2 seconds, its velocity is 6 meters per second. What is the acceleration of the ball? What do we know? What do we want to know? What formula should we use? Solve!

Ex. 2) A car traveling at 10 m/s starts to decelerate steadily Ex. 2) A car traveling at 10 m/s starts to decelerate steadily. It comes to a complete stop in 20 seconds. What is its acceleration? What do we know? What do we want to know? What formula should we use? Solve!

Ex. 3) An airplane travels down a runway for 4 Ex. 3) An airplane travels down a runway for 4.0 seconds with an acceleration of 9.0 m/s^(2). What is its change in velocity during this time? What do we know? What do we want to know? What formula should we use? Solve!

Ex. 4) A child drops a ball from a bridge Ex. 4) A child drops a ball from a bridge. The ball strikes the water under the bridge 2.0 seconds later. What is the velocity of the ball when it strikes the water? What do we know? What do we want to know? What formula should we use? Solve!

Ex. 5) A boy throws a rock straight up into the air Ex. 5) A boy throws a rock straight up into the air. It reaches the highe4st point of its flight after 2.5 seconds. How fast was the rock going when it left the boys hand? What do we know? What do we want to know? What formula should we use? Solve!

C. Graphs of accelerated motion A. You can use a speed time graph to calculate acceleration. It’s easy!!! B. The slope of a speed time graph is acceleration! C. The slope is the change in speed divided by the change in time.

D. Find the acceleration 16 12 8 4 0 1 2 3 4

D. Find the acceleration 5 4 3 2 1 0 5 10 15 20