Describing Motion Acceleration Motion & Forces Describing Motion Acceleration

v d t Speed & Velocity Speed rate of motion distance traveled per unit time

Speed & Velocity Instantaneous Speed Average Speed speed at a given instant Speedometer Average Speed

Speed & Velocity Velocity speed in a given direction can change even when the speed is constant!

t a Acceleration Acceleration a: acceleration vf: final velocity vf - vi t Acceleration the rate of change of velocity change in speed or direction a: acceleration vf: final velocity vi: initial velocity t: time

Acceleration, Speed and Velocity When you think of acceleration, you probably think of something speeding up. However, an object that is slowing down also is accelerating. Acceleration also has direction, just as velocity does

Acceleration If the acceleration is in the same direction as the velocity, the speed increases and the acceleration is positive.

Acceleration If the speed decreases, the acceleration is in the opposite direction from the velocity, and the acceleration is negative.

Changing Direction A change in velocity can be either a change in how fast something is moving or a change in the direction of movement. Any time a moving object changes direction, its velocity changes and it is accelerating.

Changing Direction The speed of the horses in this carousel is constant, but the horses are accelerating because their direction is changing constantly.

Acceleration Positive acceleration “speeding up” Negative acceleration “slowing down”

t a Calculations t = 3 s vf = 32 m/s a = ? vi = 10 m/s GIVEN: WORK: A roller coaster starts down a hill at 10 m/s. Three seconds later, its speed is 32 m/s. What is the roller coaster’s acceleration? GIVEN: vi = 10 m/s t = 3 s vf = 32 m/s a = ? WORK: a = (vf - vi) ÷ t a = (32m/s - 10m/s) ÷ (3s) a = 22 m/s ÷ 3 s a = 7.3 m/s2 a vf - vi t

t a Calculations t = 12 s vf = 6.7 m/s a = ? vi = 0 m/s GIVEN: WORK:   A skater goes from a standstill to a speed of 6.7 m/s in 12 seconds.  What is the acceleration of the skater? GIVEN: vi = 0 m/s t = 12 s vf = 6.7 m/s a = ? WORK: a = (vf - vi) ÷ t a = (6.7m/s - 0m/s) ÷ (12s) a = 6.7 m/s ÷ 12 s a = .56 m/s2 a vf - vi t

t a Calculations a = (vf - vi) ÷ t t = 5 s a = (0m/s - 9m/s) ÷ (5s) As a shuttle bus comes to a normal stop, it slows from 9.00m/s to 0.00m/s in 5.00s.  Find the average acceleration of the bus.       GIVEN: vi = 9 m/s t = 5 s vf = 0 m/s a = ? WORK: a = (vf - vi) ÷ t a = (0m/s - 9m/s) ÷ (5s) a = -9 m/s ÷ 5 s a = -1.8 m/s2 a vf - vi t

Calculations How long will it take a car traveling 30 m/s to come to a stop if its acceleration is -3 m/s2? GIVEN: t = ? vi = 30 m/s vf = 0 m/s a = -3 m/s2 WORK: t = (vf - vi) ÷ a t = (0m/s-30m/s)÷(-3m/s2) t = -30 m/s ÷ -3m/s2 t = 10 s a vf -vi t

Amusement Park Acceleration Engineers use the laws of physics to design amusement park rides that are thrilling, but harmless. The highest speeds and accelerations usually are produced on steel roller coasters.

Amusement Park Acceleration Steel roller coasters can offer multiple steep drops and inversion loops, which give the rider large accelerations. As the rider moves down a steep hill or an inversion loop, he or she will accelerate toward the ground due to gravity.

Amusement Park Acceleration When riders go around a sharp turn, they also are accelerated. This acceleration makes them feel as if a force is pushing them toward the side of the car.