vf - vi a = t Acceleration Acceleration is another way to measure and describe the motion of an object. Acceleration: (a) rate of change of velocity over time. An object is considered to be accelerating when it speeds up, slows down, or changes direction. Measured in mi/hr2, m/s2, km/hr2, etc. Positive acceleration: when an object speeds up Negative acceleration: when an object slows down. vf - vi a = t vf = final velocity vi = initial velocity

Example #1 A car traveling 35 km/hr accelerates to a speed of 45 km/hr in 0.25 hr. What is its acceleration? vi = 35 km/hr vf = 45 km/hr t = 0.25 hr a = ? a = vf - vi t a = (45 – 35) 0.25 a = 10 . a = 40 km/hr2

Example #2 A jet is traveling at 80 m/s when it starts to approach a runway. It is able to land and park in 10 s. What is its acceleration? vi = 80 m/s vf = 0 m/s t = 10 s a = ? a = vf - vi t a = (0 – 80) 10 a = -80 . a = -8 m/s2 The negative acceleration makes sense because the jet is slowing down as it comes to a stop.

Example #3 A skateboarder has an acceleration of 1.5 m/s2. Starting from rest, if he accelerates for 2 s, what speed will he reach? a = 1.5 m/s2 vi = 0 m/s t = 2 s vf = ? a = vf - vi t at = vf – vi at + vi = vf vf = at + vi vf = (1.5)(2) + 0 vf = 3 + 0 vf = 3 m/s Definitely a required question for honors or could be bonus for CP! (t) (t) + vi + vi

Practice Time A car accelerates from a standstill to 60 km/s in 10 s. What is its acceleration? A car accelerates from 25 mi/hr to 55 mi/hr in 0.0083 hr. What is its acceleration? A runner has a velocity of 11.1 m/s for 9 seconds until he finishes the race and comes to a stop. What is his acceleration? A motorcyclist has an acceleration of 5 mi/hr2. If his initial velocity is 45 mi/hr, what is his final velocity after 4 hours? Answer: a = 6 km/s2 Answer: a = 3,614.5 mi/hr2 I have students work these out in their notes and I walk around and help them as they work. Then we go over the answers all together. I especially encourage CP students that if they don’t know what to do, they at least need to set up the problem (labeling values that they know and writing the appropriate equation.). They should NEVER leave a problem blank! Answer: a = -1.23 m/s2 Answer: vf = 65 mi/hr

Graphing Acceleration Graphs can visually help us to understand an object’s motion. Remember… Slope: the steepness of a line. Calculated as rise = Δy run Δx On a velocity vs. time graph, this means… Calculated as rise = Δy = velocity run Δx time Therefore on a velocity vs. time graph, the slope = acceleration.

Graphing Acceleration Describe the acceleration of the object in each graph. The object is moving at a constant speed, therefore it has 0 acceleration The object is not moving, therefore it has 0 acceleration The object is slowing down, therefore it has a negative acceleration The object is speeding up, therefore it has a positive acceleration

Graphing Acceleration You can also describe the acceleration of an object by looking at distance vs. time graphs. The object is moving at a constant speed, therefore it has 0 acceleration The object is not moving, therefore it has 0 acceleration The object is slowing down, therefore it has a negative acceleration The object is speeding up, therefore it has a positive acceleration