Acceleration

Acceleration The rate at which an object is changing its velocity Click for Definition The rate at which an object is changing its velocity An object is accelerating if: 1) It is speeding up 2) It is slowing down 3) It is changing direction Click Click Click Click for Reminders: it is important to remember that velocity is a vector quantity, so therefore acceleration is also a vector quantity (even though we don’t always mention direction) sometimes the direction of acceleration is implied with the negative sign (-) or a positive sign (+)

Changing Direction? Obviously if an object is speeding up or slowing down, its velocity is changing, so it must be accelerating in some manner, but why is an object accelerating when changing direction? Click on car You must remember that acceleration is technically a vector quantity and therefore includes amount and direction. Therefore, if direction changes, even if speed (velocity) does not change, acceleration changes.

Positive and Negative Acceleration Positive Acceleration (click) If an object is speeding up, it is accelerating in the same direction as its velocity. Therefore, it has positive acceleration. Negative Acceleration (click) If an object is slowing down, it is accelerating in the direction opposite that of its velocity. Therefore, it has negative acceleration. Negative acceleration is also called deceleration

Calculating Acceleration Because acceleration is defined as the rate of change in an object’s velocity, acceleration can also be thought of as a change in velocity compared to the change in time. Click on the following formula to calculate acceleration: final velocity – initial velocity time acceleration = -- OR -- vf – vi t a = Note that we represent final and initial velocity using the subscripts f and i on velocity’s v

What does this formula mean? If final velocity is > initial velocity, the equation vf – vi will be positive, giving you a positive answer for acceleration, meaning that the object is accelerating positively (gaining speed/velocity) Click for example 40m/s – 10m/s = 30m/s If final velocity is < initial velocity, the equation vf – vi will be negative, giving you a negative answer for acceleration, meaning that the object is decelerating (losing speed/velocity) Click for example 30m/s – 50m/s = -20m/s ***Time can never be a negative number (we cannot lose time)***

Units “meters per second squared” Because the units for velocity are meters per second (m/s) and the units for time are seconds (s), acceleration is found by the equation: Click m/s m s s s a = = Which equals m/s2 Read aloud as: (click) “meters per second squared”

Many times, if no initial velocity is given, vi = 0 m/s Problem Solving Because acceleration problems can be challenging, it is often a good idea to write out all of your variables before you solve. Many times, if no initial velocity is given, vi = 0 m/s

Practice Problems 1. A car is stopped at a red light. The light turns green, and the car accelerates to a velocity of 20 m/s in 5 seconds. What is the acceleration of the car? 2. A car is traveling at 45 m/s on the freeway when it sees a police car on the horizon. What is the deceleration of the car so that it gets to a speed of 30 m/s in the 5 seconds it takes to reach the cop? vf – vi t a = Click for formula Click for setup Click for answer 20m/s-0m/s 5s 4m/s2 Click for setup vf – vi t a = Click for formula 30m/s - 45m/s 5s Click for answer -3m/s2

More Practice Problems On Earth, falling objects accelerate at a rate of 9.8 m/s2. How long does it take a skydiver who jumped from a plane to reach a velocity of 196 m/s? A motorcycle accelerates at a rate of 7 m/s2 for 8 seconds. If the initial velocity of the motorcycle before it accelerates was 11 m/s East, what is the new velocity of the motorcycle after acceleration? Click for setup 196m/s – 0m/s t Click for answer Click for formula vf – vi t a = 9.8m/s2 = 20s vf – vi t a = Click for formula Click for setup vf – 11m/s 8 Click for answer 67m/s 7m/s2 =