Chapter 2 Uniformly Accelerated Motion Speed Velocity Acceleration
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Chapter 2 Uniformly Accelerated Motion
Speed
Velocity
Acceleration What are the units for acceleration?
Uniformly Accelerated Motion Along a Straight Line t 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 t Draw a sketch – Indicate origin and positive direction t List the given quantities using the symbols of the equatio – Is time known or do we need to find it? – What are we to solve for? t Write the general equations of kinematics
More Guidelines t t 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 t Fifteen minutes
Definitions t Instantaneous Velocity – the slope of the displacement versus time graph t Instantaneous Acceleration – the slope of the velocity versus time graph
Displacement Slopes A B Time
Teaming Exercise Next Problem solutions
Free Fall t The force of gravity points downward – Acceleration of gravity near the surface of Earth is called g = 9. 8 m/s 2 = 32. 1 ft/s 2 t Air resistance ignored t We have then the conditions of onedimensional kinematics – straight line motion with constant acceleration.
Sample Problem t 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 t Ignore air resistance. t ax = 0 t ay = g = 9. 81 m/s 2 downward
The motions in the two directions are independent Horizontal Vertical
Real Motion is the Combination of the Two
2 -D Problem Guidelines t Set up two 1 -D solutions Origin x Positive x xi = vxi = ax = 0 Origin y Positive y yi = vyi = ay = g
2 -D Guidelines Cont’d t t t 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
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