Uniformly Accelerated Motion Chapter 2 Uniformly Accelerated Motion

Speed

Velocity

Acceleration What are the units for acceleration?

Uniformly Accelerated Motion Along a Straight Line In this case… acceleration is a constant and the acceleration vector lies in the line of the displacement vector.

The 5 Equations! (1) (2) (3) (4) (5)

Problem Solution Guidelines Draw a sketch Indicate origin and positive direction List the given quantities using the symbols of the equations. (si, vi, a) Is time known or do we need to find it? What are we to solve for? Write the general equations of kinematics

More Guidelines Rewrite the general equations using the known quantities. Look at the knowns and unknowns and map a strategy of solution. Check your units Make sure you are answering the question.

Problem Solution Time Fifteen minutes

Definitions Instantaneous Velocity Instantaneous Acceleration the slope of the displacement versus time graph Instantaneous Acceleration the slope of the velocity versus time graph

Slopes Displacement A B Time

Teaming Exercise Next Problem solutions

Free Fall The force of gravity points downward Air resistance ignored Acceleration of gravity near the surface of Earth is called g = 9.8 m/s2 = 32.1 ft/s2 Air resistance ignored We have then the conditions of one-dimensional kinematics – straight line motion with constant acceleration.

Sample Problem A ball is thrown vertically upward at 10 m/s. How high will it get, how long will it be in the air, and how fast will it be moving when it hits the ground.

Projectile Problems – Two Dimensional Kinematics Ignore air resistance. ax = 0 ay = g = 9.81 m/s2 downward

The motions in the two directions are independent Horizontal Vertical

Real Motion is the Combination of the Two

2-D Problem Guidelines Set up two 1-D solutions Origin x Origin y Positive x Positive y xi = yi = vxi = vyi = ax = 0 ay = g

2-D Guidelines Cont’d Write general kinematic equations for each direction Rewrite them for the problem at hand Find the condition that couples the motions (usually time)

Uniformly Accelerated Motion Along a Straight Line