Representing Motion in a Variety of Ways Graphs: - Allows us to interpret motion without even seeing the motion occur What was the object’s velocity (not speed) from 0-2 sec? +2 m/s Can we derive an equation for velocity from this graph? Or any other x-t graph? X f = vt + xi X f – Xi = vt 𝑉= (4𝑚−0𝑚) 2 𝑠 𝑉= 4 𝑚 2 𝑠 =2 𝑚/𝑠 ( 𝑋 𝑓 − 𝑋 𝑖 ) 𝑡 = V 𝑉= ∆𝑋 𝑡

Position-Time Graphs (x-t) Velocity from 2-3 seconds? 𝑉= 0 𝑚 1 𝑠 =0 𝑚/𝑠 Velocity from 3-7 seconds? 𝑉= ( 𝑋 𝑓 − 𝑋 𝑖 ) 𝑡 = (0 𝑚−4 𝑚) 4 𝑠 = −4 𝑚 4 𝑠 =−1 𝑚/𝑠

Motion Maps Another way to represent an object’s motion We can go back and forth between graphs and motion maps to represent the same motion To make a motion map, you need to draw an arrow representing positive direction Constant positive velocity X Beginning of the arrow is the reference point (origin) If the object is moving, its position will change over time. If the object is stationary, its position will remain the same as time increases On a motion map, this is illustrated by a single dot on the position arrow

Motion Maps Object is stationary X An object’s constant velocity is indicated by 2 things: The displacement between the points are constant (change in position is equal) Arrows indicating the object’s velocity are the same length Constant positive velocity X If the object is stationary, then the velocity is zero and there is not an arrow indicating velocity X

More than one object How do we know which object is traveling faster? slope: remember, slope = velocity Steeper the slope, faster the velocity B X (m) A Object B has a greater displacement (change in position) than A IN THE SAME AMOUNT OF TIME 2 t (sec)

Review from yesterday ∆𝑥=( 𝑥 𝑓 − 𝑥 𝑖 ) Slope = ∆𝑥 𝑡 =𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 Y-intercept = starting position Slope = ∆𝑥 𝑡 =𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 Velocity IS NOT THE SAME as speed Speed How fast Velocity How fast direction X X

Consider the following x-t graphs Rank these situations from greatest to least based on which shows the greatest displacement during the time from 0 to 10 sec. Use the > and = signs, but do not use the < sign. Rank these situations from greatest to least based on which shows the greatest distance traveled during the time from 0 to 10 sec. Use the > and = signs, but do not use the < sign.