Acceleration When an object moves, most of the time it’s motion (velocity) will not be constant. Whenever an object changes it’s velocity (speed with a direction) the object has what is called an acceleration. An object has an acceleration whenever it… Speeds up Slows down Changes direction An acceleration is how fast the velocity of an object changes. Since velocity is a vector, acceleration is also a vector.

Instantaneous and Average Acceleration There are two types of acceleration: Average acceleration– This is how fast an object changes it’s velocity over a period of time. Instantaneous acceleration– How fast an object changes it’s velocity at a given point in time. A car drives speeds up from 0 to 50 MPH in 5 seconds. This takes place in 5 seconds time so this is an average. This is an average acceleration A rock is dropped, and accelerates downward at 9.8 m/s/s when released. The rock accelerates at 9.8 m/s/s at THE INSTANT it is released. This is an instantaneous acceleration.

Calculating Average Acceleration Acceleration is how fast the velocity changes. It is the change in velocity in a given time. Change in Velocity Average Acceleration = ------------------------- Time for the change The Units for acceleration can be any unit of velocity (speed) divided by a unit of time. Units for Acc: (Meters/sec)/sec or Meters/sec2 (Miles/Hr.)/sec (Feet/min)/sec (Kilometers/Hr.)/min Acc. Time Vf -Vi

Using the acceleration box to find the average acceleration A Girl starts from rest and accelerates to a running speed of 8 m/s in a time of .5 seconds. What is her average acceleration? Next cover up the part of the box you are looking for. The equation you want is: Vf - Vi Acc = ------------------- Time Acc. Vf -Vi Finally substitute the numbers into the equation and solve. Vf -Vi Acc = ------------------- Time 8 m/s – 0 m/s Acc = --------------------- = 16 m/s/s or 16 m/s2 .5 sec Acc. First write out the box Acc. Time Vf -Vi

Using the acceleration box to find the time needed to accelerate A car traveling at 6 m/s accelerates at a rate of 4m/s2. How much time will it take to reach a speed of 14 m/s? Finally substitute the numbers into the equation and solve. Vf -Vi Time = ------------------- Acc 14 m/s – 6 m/s 8m/s Time = --------------------- = ----------- = 2 sec 4 m/s2 4 m/s2 Acc. Time Next cover up the part of the box you are looking for. The equation you want is: Vf - Vi Time = ------------------- Acc Acc. Time Vf -Vi First write out the box Acc. Time Vf -Vi

Using the acceleration box to find the final velocity (speed). A rock is dropped and falls with a constant acceleration of –9.8 m/s2. What will the rock’s velocity be 5 seconds into the fall? Finally substitute the numbers into the equation and solve. Vf = Acc*Time + Vi Vf = -9.8 m/s2 * 5 s + 0 m/s Vf = - 49 m/s ( - means DOWN) Acc. Time Vf -Vi Next cover up the part of the box you are looking for. The equation you want is: Vf – Vi = Acc. * Time which becomes Vf = Acc*Time + Vi Acc. Time Vf -Vi First write out the box Acc. Time Vf -Vi

Using the acceleration box to find the Initial velocity (speed). A ball is rolled across a floor with with an unknown speed, and comes to a complete stop in 5 seconds. If the acceleration of the ball is -.5 m/s2, what was the initial speed of the ball? Finally substitute the numbers into the equation and solve. Vi = -(Acc*Time + Vf) Vi = -(-.5 m/s2 * 5 s + 0 m/s) Vi = + 2.5 m/s2 Acc. Time Vf -Vi Next cover up the part of the box you are looking for. The equation you want is: Vf – Vi = Acc. * Time which becomes - Vi = Acc*Time – Vf Multiply both sides by –1 Vi = -(Acc*Time – Vf) Acc. Time Vf -Vi First write out the box Acc. Time Vf -Vi

Picturing Acceleration Let us say that there is a ball that rolls from rest with a constant acceleration of 2m/s2. What would the ball’s motion look like second by second? 0 m .5m 2 m 4.5 m 8 m

Graphing the Displacement of Acceleration We can construct a data table and a position verse time graph for the motion. Position (m) Time (sec) Time (seconds) Position (meters) 1 2 3 4 .5 4.5 8 The position verses time graph for accelerated motion will ALWAYS be a parabola. The is because the velocity (the slope) is always changing.

Speeding Up, Slowing Down If you are speeding up parabola becomes more curved. That is because the distance traveled each second increases more and more. Position (m) Time (sec) Moving in a positive direction Position (m) Time (sec) Moving in a negative direction If you are slowing down the parabola becomes less curved. That is because the distance traveled each second becomes less and less. Position (m) Time (sec) Moving in a negative direction Position (m) Time (sec) Moving in a positive direction

Graphing the Velocity of an Accelerated Object Vf -Vi Acc = ---------------- Time Let’s start with the acceleration equation We can rewrite the acceleration equation Vf = acc*time + Vi Now compare it to The equation for a straight line y = m*x + b They are the same!!! Y = Vf M = slope = acceleration B = intercept = Vi

Graphing the Velocity of an Accelerated Object This means that the velocity graph for a object moving with a constant acceleration is a straight line. THE SLOPE OF THE LINE, IS THE ACCLERATION!!!! time Vel. A positive slope means a positive acceleration. time Vel. A negative slope means a negative acceleration.

Remember +/- means direction An object can have a negative acceleration and still pick up speed. If the object already has a negative velocity. V t An object can have a positive acceleration and slow down. If the object started with a negative velocity. V t Important note: If the velocity line moves away from the time (X) axis the object is speeding up. If the velocity line moves to the time (X) axis the object is slowing down.