F08_Lect02 - Physics 112 Lecture 2 Agenda for Today 1-D...

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Physics 112: Lecture 2 Agenda for Today 1-D Kinematics 1-D Kinematics – Average & instantaneous velocity and acceleration – Motion with constant acceleration
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Motion in 1 dimension In 1-D, we usually write position as x(t). Since it’s in 1-D, all we need to indicate direction is + or . Displacement in a time Δ t = t 2 - t 1 is Δ x = x(t 2 ) - x(t 1 ) = x 2 - x 1 t x t 1 t 2 Δ x Δ t x 1 x 2 some particle’s trajectory in 1-D
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1-D kinematics t x t 1 t 2 Δ x x 1 x 2 trajectory • Velocity v is the “rate of change of position” Average velocity v av in the time Δ t = t 2 - t 1 is: Δ t V av = slope of line connecting x 1 and x 2 . v av " x ( t 2 ) # x ( t 1 ) t 2 # t 1 = $ x $ t
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Consider limit t 1 t 2 Instantaneous velocity v is defined as: 1-D kinematics... t x t 1 t 2 Δ x x 1 x 2 Δ t so v(t 2 ) = slope of line tangent to path at t 2 . v ( t ) = dx ( t ) dt
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You are driving on a highway at 80 km/h for 5 h and then through a town at 20 km/h for 30 minutes. What is your average velocity (assume that it’s all in one direction)? Average velocity: a common mistake
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Average velocity: a common mistake You are driving on a highway at 80 km/h for 5 h and then through a town at 20 km/h for 30 minutes. What is your average velocity (assume that it’s all in one direction)? Wrong: (v1 + v2)/2 = 50 km/h Correct: total distance / total time = (400 km + 10 km) / (5 h + 0.5h) = 74.5 km/h
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Graph of x(t) versus time, what’s the average velocity?
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Definition of SPEED: distance traveled without regard to direction, divided by time t. What’s the average speed?
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