2. Notes on Motion IV Acceleration a

3. What do you think of when someone says acceleration? If you think speeding up – then you are almost completely correct!!!! It turns out that an object is accelerating if it Speeds up Slows down Or changes direction

4. Defining Acceleration Acceleration is defined as the rate of change of velocity. Another way to say this is that acceleration measures how fast an objects velocity changes. Accelerations can be positive or negative But Positive acceleration doesn’t always mean an object is speeding up. Negative acceleration doesn’t always mean an object is slowing down.

5. Speeding Up or Slowing Down For linear motion (straight-line). Whether or not an object speeds up or slows down is determined by the direction of the acceleration COMPARED to the direction of motion (velocity). If an object is moving in the positive direction and its acceleration is also positive, then the object will speed up. v a If an object is moving in the negative direction and its acceleration is also negative, then the object will speed up. v a If an object is moving in the positive direction and its acceleration is also negative, then the object will slow down. v a If an object is moving in the negative direction and its acceleration is also positive, then the object will slow down. v a In general, if the acceleration and velocity have the same sign (both positive or both negative), then the object: SPEEDS UP In general, if the acceleration and velocity have different signs (one positive and one negative), then the object: SLOWS DOWN

6. Units for Acceleration English System Feet per Second per Second (ft/s/s or ft/s 2 ) Metric System Kilometers per Hour per second (km/hr/s), Meters per Second per Second (m/s/s or m/s 2 )) In science the most common unit is: m/s/s or m/s 2

7. Meaning of Acceleration A car starts from rest and accelerates at 4 km/hr/s. What does this mean? This means the car’s velocity changes by 4 km/hr each second. Starting Velocity: Velocity after 1-s: Velocity after 2-s: Velocity after 10-s: 0 km/hr 4 km/hr 8 km/hr 40 km/hr

8. Meaning of Acceleration A car traveling at 10 km/hr accelerates at 4 km/hr/s. What does this mean? This means the car’s velocity changes by 4 km/hr each second. Starting Velocity: Velocity after 1-s: Velocity after 2-s: Velocity after 10-s: 10 km/hr 14 km/hr 18 km/hr 50 km/hr

9. Meaning of Acceleration A car traveling at 8 km/hr accelerates at-4 km/hr/s. What does this mean? This means the car’s velocity changes by -4 km/hr each second. Starting Velocity: Velocity after 1-s: Velocity after 2-s: Velocity after 10-s: 8 km/hr 4 km/hr 0 km/hr -32 km/hr STOPPED!!!!!! CHANGED DIRECTIONS

10. Solving Problems with Acceleration Acceleration is defined as the rate of change of velocity. Since this is a rate of change we can also say that acceleration is the change in velocity over time. As an equation this looks like: v f is the final velocity (ending) and v i is the initial velocity (starting). This will find the average acceleration if the change in velocity is over a time interval. This will find the uniform acceleration if the acceleration is constant.

11. Solving Problems with Acceleration If we place his formula into our triangle, we can find other useful formulas from this v f - v i at

12. Solving Problems with Velocity and Speed at If you need to find t, cover t. Since v f - v i is on top of a, divide them. v f - v i

13. Solving Problems with Velocity and Speed at If you need to find v f, cover v f -v i. Since a is next to t, multiply them. Finally add v i to both sides. v f - v i

14. Solving Problems with Acceleration v f - v i at Example Problem 1: A car is travelling at 15-m/s when it begins to pass a slower car. The car accelerates to 20-m/s in 0.5-s. What is the car’s acceleration? Know: v i = 15-m/s v f = 20-m/s t = 0.5-s Find: a = ? Formula: Solve:

15. Solving Problems with Acceleration v f - v i at Example Problem 2: A car is traveling at 25-m/s when its brakes are applied slowing it to a stop. This takes 2.0-s. What is the acceleration of the car? Know: v i = 25-m/s v f = 0-m/s t = 2.0-s Find: a = ? Formula: Solve:

16. Solving Problems with Acceleration v f - v i at Example Problem 3: How long would it take a car starting from rest to reach a speed of 45-m/s if it accelerates at 5.0–m/s 2 ? Know: v i = 0-m/s v f = 45-m/s a = 5.0–m/s 2 Find: t = ? Formula: Solve:

17. Solving Problems with Acceleration v f - v i at Example Problem 4: A sprinter starts from rest and accelerates at 3.5-m/s 2 for 9.5-s. What is the runners speed after that time? Know: v i = 0-m/s t = 9.5-s a = 3.5–m/s 2 Find: v f = ? Formula: Solve: