Motion & Forces Describing Motion  Acceleration

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

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

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

Acceleration, Speed and Velocity Acceleration is the rate of change of velocity. When the velocity of an object changes, the object is accelerating. Acceleration is the rate of change of velocity. When the velocity of an object changes, the object is accelerating. A change in velocity can be either a change in speed something is moving, or a change in the direction it is moving. A change in velocity can be either a change in speed something is moving, or a change in the direction it is moving. Acceleration occurs when an object changes its speed, it's direction, or both. Acceleration occurs when an object changes its speed, it's direction, or both.

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

Calculating Acceleration To calculate the acceleration of an object, the change in velocity is divided by the length of time interval over which the change occurred. To calculate the acceleration of an object, the change in velocity is divided by the length of time interval over which the change occurred. To calculate the change in velocity, subtract the initial velocity—the velocity at the beginning of the time interval—from the final velocity—the velocity at the end of the time interval. To calculate the change in velocity, subtract the initial velocity—the velocity at the beginning of the time interval—from the final velocity—the velocity at the end of the time interval.

Calculating Acceleration Then the change in velocity is: Then the change in velocity is:

Acceleration Acceleration Acceleration the rate of change of velocity the rate of change of velocity change in speed or direction change in speed or direction a: acceleration v f : final velocity v i : initial velocity t: time a v f - v i t

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

Calculations 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? 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: v i = 10 m/s t = 3 s v f = 32 m/s a = ? WORK : a = (v f - v i ) ÷ t a = (32m/s - 10m/s) ÷ (3s) a = 22 m/s ÷ 3 s a = 7.3 m/s 2 a v f - v i t

Calculations A skater goes from a standstill to a speed of 6.7 m/s in 12 seconds. What is the acceleration of the skater? 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: v i = 0 m/s t = 12 s v f = 6.7 m/s a = ? WORK : a = (v f - v i ) ÷ t a = (6.7m/s - 0m/s) ÷ (12s) a = 6.7 m/s ÷ 12 s a =.56 m/s 2 a v f - v i t

Calculations 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 : v i = 9 m/s t = 5 s v f = 0 m/s a = ? WORK : a = ( v f - v i ) ÷ t a = (0m/s - 9m/s) ÷ (5s) a = -9 m/s ÷ 5 s a = -1.8 m/s 2 a v f - v i t

Calculations Calculations How long will it take a car traveling 30 m/s to come to a stop if its acceleration is -3 m/s 2 ? GIVEN: t = ? v i = 30 m/s v f = 0 m/s a = -3 m/s 2 WORK: t = (v f - v i ) ÷ a t = (0m/s-30m/s)÷(-3m/s 2 ) t = -30 m/s ÷ -3m/s 2 t = 10 s a v f -v i t

Amusement Park Acceleration Engineers use the laws of physics to design amusement park rides that are thrilling, but harmless. 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. 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. 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. 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. 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. This acceleration makes them feel as if a force is pushing them toward the side of the car.