Acceleration describes how an object's velocity changes over time. An object accelerates when its speed changes, its direction changes, or both its speed and direction change. Acceleration is calculated by taking the change in velocity and dividing by the time elapsed. Common examples of acceleration include objects falling due to gravity, objects moving in circles due to centripetal force, and vehicles changing speed.

1. Acceleration

2. In the real world, objects move with changing velocities. A new concept called acceleration has been defined to describe how velocity changes. Acceleration is change in velocity with respect to time. Velocity can change in three ways: (a) change in speed, either increase or decrease ; (b) change in direction; and (c) change in speed as well as direction. Thus , an object is said to be accelerating when it either moving with changing speed, moving with constant speed but with changing direction, or moving with changing speed as well as changing direction. acceleration = change in velocity time a= ∆ v ∆t Since acceleration is defined in terms of velocity, it is also a vector quantity. The SI unit of acceleration is meter per second per second, m/s/s or m/s 2.

3. Changes in Speed Falling objects accelerate in response to the force exerted on them by Earth’s gravity. Different objects accelerate at the same rate, regardless of their mass. This illustration shows the speed at which a ball and a cat would be moving and the distance each would have fallen at intervals of a tenth of a second during a short fall.

4. Changes in Direction When a ball is whirled in a circle, it is accelerating inward . This inward acceleration is caused by a centripetal , or center-seeking, force supplied by the tension in the string. The required force is equal to mv 2 / r , where m is the mass of the ball, v is its velocity (speed and direction), and r is its distance from the center of revolution .

5. Change in Velocity Each time you take a step you are changing the velocity of your body. You are probably most familiar with the velocity changes of a moving bus or car. The rate at which velocity (speed or direction) changes occur is called acceleration.

6. Changes in both Speed and Direction Acceleration often involves both a change in speed and a change in direction. Changing both components of velocity results in a curved path of motion. In these cases, the acceleration vector is the sum of two parts (components). One part, the tangential acceleration, acts along the direction of motion, parallel to the velocity, resulting in a change of speed. The other part, the radial acceleration, acts perpendicular to the direction of motion, resulting in a change of direction. In order to change the speed of an object moving in a circle, for example, one needs some acceleration along the direction of motion, in addition to the component of acceleration in the radial direction (pointing to the center) that keeps the object moving in a circle. In the case of a space shuttle in orbit, the radial acceleration is the force of gravity pulling the shuttle toward Earth, while a tangential acceleration is achieved by firing rockets along the direction of motion.

7. Acceleration= final velocity- starting velocity time Change in velocity = final – starting velocity velocity Acceleration= change in velocity time

8. Acceleration = Velocity (final) - Velocity (original) time A car traveling at 60 mph accelerates to 90 mph in 3 seconds. What is the car’s acceleration? = 90 mph - 60 mph 3 seconds = 30 mph 3 seconds = 10 mph/second

9. Positive acceleration Negative acceleration

10. Acceleration = Velocity (final) - Velocity (original) time A car traveling at 60 mph slams on the breaks to avoid hitting a deer. The car comes to a safe stop 6 seconds after applying the breaks. What is the car’s acceleration? = 0 mph - 60 mph 6 seconds = - 60 mph 6 seconds = - 10 miles per hour per second

11. - A constant acceleration produces a straight line or linear slope (rise/run). - The slope of a non-linear velocity-time graph (rise/run) will predict an objects instantaneous acceleration. a = v/t

12. Galileo 1600’s Studied how things fell Didn’t have a good clock Rolled balls down an inclined plane Found that the speed increased as it rolled down the ramp

13. Galileo Acceleration= change in velocity time t = 0 t = 1 second t = 2 seconds t = 3 seconds

14. Galileo Same things happen when things fall Didn’t drop things from Tower of Pisa

15. v 2 final = 2gd y A final velocity can be calculated over a vertical displacement “d y " during free fall using the equation:

16. d y = 1/2 gt 2 The vertical displacement “d y " that occurs during a specific time of free fall can be determined using the equation: Or a time interval can also be determined over a specified distance of freefall using the equation: t 2 = 2d y /g

17. Falling Air resistance will increase as it falls faster An upward force on the object Eventually gravity will balance with air resistance Reaches terminal velocity - highest speed reached by a falling object.

18. Terminal velocity Force of gravity is constant air resistance increases as you speed up until the force is equal Equal forces, no acceleration constant velocity terminal velocity

19. THE END! 