Section 3: Acceleration Acceleration describes how the velocity of an object is changing with time. K What I Know W What I Want to Find Out L What I Learned

Essential Questions How are acceleration, time, and velocity related? What are three ways an object can accelerate? How can an object’s acceleration be calculated? What are the similarities and differences between straight line motion, circular motion, and projectile motion? Copyright © McGraw-Hill Education Acceleration

Vocabulary Review New velocity acceleration centripetal acceleration Copyright © McGraw-Hill Education

Acceleration, Speed and Velocity 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 how fast something is moving or a change in the direction it is moving. Acceleration occurs when an object changes its speed, its direction, or both. Copyright © McGraw-Hill Education Acceleration

Speeding Up and Slowing Down If the acceleration is in the same direction as the velocity, the speed increases. Acceleration Copyright © McGraw-Hill Education

Speeding Up and Slowing Down If the speed decreases, the acceleration is in the opposite direction from the velocity, and the acceleration is negative. Acceleration Copyright © McGraw-Hill Education

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 change in velocity, subtract the initial velocity (vi)—the velocity at the beginning of the time interval—from the final velocity—the velocity at the end of the time interval (vf). ­ Copyright © McGraw-Hill Education Acceleration

Calculating Acceleration Using this expression for the change in velocity, the acceleration can be calculated from the following equation: Acceleration Copyright © McGraw-Hill Education

CALCULATE ACCELERATION SOLVE FOR THE UNKNOWN Set Up the Problem a = (vf –vi ) t = (0 m/s – 3 m/s) 2 s west Solve the Problem a = (0 m/s – 3 m/s) 2 s = – 1.5 m/s2 west The acceleration has a negative sign, so the direction is reversed. a = – 1.5 m/s2 east Use with Example Problem 3. Problem A skateboarder has an initial velocity of 3 m/s west and comes to a stop in 2 s. What is the skateboarder’s acceleration? Response ANALYZE THE PROBLEM KNOWN initial velocity: vi = 3 m/s west final velocity: vf = 0 m/s west time: t = 2 s UNKNOWN acceleration: a EVALUATE THE ANSWER The magnitude of the acceleration (1.5 m/s2) is reasonable for a skateboard that takes 2 s to slow from 3 m/s to 0 m/s. The acceleration is in the opposite direction of the velocity, so the skateboard is slowing down, as we expected. Copyright © McGraw-Hill Education Acceleration

Speeding Up Suppose a car starts at rest and reaches a speed of 80 m/s as it heads east down the street. Its acceleration can be calculated as follows: Acceleration Copyright © McGraw-Hill Education

The final speed is zero and the initial speed was 3 m/s. Slowing Down Now imagine a skateboarder is moving in a straight line with a velocity of 3 m/s north and comes to a stop in 2 s. The final speed is zero and the initial speed was 3 m/s. Copyright © McGraw-Hill Education Acceleration

Calculating Negative Acceleration The skateboarder's acceleration is calculated as follows: The acceleration is in the opposite direction of the skateboard’s velocity when the skateboarder is slowing down. Copyright © McGraw-Hill Education Acceleration

Changing Direction The speed of the horses in this carousel is constant, but the horses are accelerating because their direction is changing constantly. Acceleration toward the center of a curved or circular path is called centripetal acceleration. Acceleration Copyright © McGraw-Hill Education

Projectile Motion Anything thrown or shot through the air is called a projectile. Projectiles follow a curved path because they have horizontal and vertical velocities. The projectile’s horizontal velocity is constant. It has vertical velocity downward due to gravity. Acceleration Copyright © McGraw-Hill Education

Review Essential Questions Vocabulary How are acceleration, time, and velocity related? What are three ways an object can accelerate? How can an object’s acceleration be calculated? What are the similarities and differences between straight line motion, circular motion, and projectile motion? Vocabulary acceleration centripetal acceleration Copyright © McGraw-Hill Education Acceleration