Methods of Motion -Acceleration AP Physics

Average Acceleration Acceleration is the RATE at which VELOCITY changes. A truck accelerates from 10 m/s to 30 m/s in 2.0 seconds. What is the acceleration? Suppose the same truck then slows down to 5 m/s in 2 seconds. What is the acceleration? “m/s/s” or “m/s2” is the derived unit for acceleration.

What do the “signs”( + or -) mean? Quantity Positive Negative Displacement You are traveling north, east, right, or in the +x or +y direction. You are traveling south, west, left, or in the –x or –y direction. Velocity The rate you are traveling north, east, right, or in the +x or +y direction. The rate you are traveling south, west, left, or in the –x or –y direction. Acceleration Your speed is increasing in a positive direction or your speed is decreasing in a negative direction. Your speed is decreasing in a positive direction or your speed is increasing in a negative direction. Show velocity/acceleration vectors – Scientists and Engineers fig 2.9

Beware – the signs can confuse! Suppose a ball is thrown straight upwards at 40 m/s. It takes 4 seconds to reach its maximum height, then another 4 seconds back down to the point where it was thrown. Assume it is caught with the same speed it was thrown. Calculate the acceleration upwards and downwards. This negative sign came from using the DELTA This negative sign came from the DIRECTION of the velocity. It is no surprise you get a negative answer both ways as gravity acts DOWNWARDS no matter if the ball goes up or down. It is GRAVITY which changes the ball’s velocity.

Instantaneous Velocity Instantaneous velocity is a measure of an object’s displacement per unit time at a particular point in time. On an x v. t graph, slope of a line at a given point is the instantaneous velocity. The term velocity alone means instantaneous velocity. All motion is translational?

Instantaneous Acceleration Instantaneous acceleration is a measure of an object’s velocity per unit time at a particular point in time. On a vel v. t graph, slope of a line at a given point is the instantaneous acceleration. The term acceleration means instantaneous acceleration.

Graphing Summary v (m/s) a (m/s/s) x (m) t (s) t (s) t (s) slope = v slope = a area = Δv area = Δx t (s) t (s) t (s)

Graphing Activity Analyze the motion of the following cars with position, velocity, and acceleration graphs. Sketch your predictions on the whiteboards. Things to consider: Constant velocity? Constant acceleration?

The 3 Kinematic Equations There are 3 major kinematic equations than can be used to describe the motion in DETAIL. All are used when the acceleration is CONSTANT.

Constant Acceleration When acceleration is constant the average velocity is just the average of the initial and final velocity values.

Calculus of Kinematics Derivative Slope on a graph Integral Area under curve on a graph Don’t forget limits of integration

Kinematics -Free Fall AP Physics

“g”– The Acceleration due to gravity The acceleration due to gravity is a special constant that exists in a VACUUM, meaning without air resistance. If an object is in FREE FALL, gravity will CHANGE an objects velocity by 9.8 m/s every second. The acceleration due to gravity: ALWAYS ACTS DOWNWARD IS ALWAYS CONSTANT near the surface of Earth

Kinematics for the VERTICAL Direction All 3 kinematics can be used to analyze one dimensional motion in either the X direction OR the y direction.

Acceleration of gravity units g – represents acceleration g – gravitational field interactions All objects accelerate towards Earth, under free-fall conditions, at the same rate. Gravitational fields force masses to move in a direction towards Earth.