Interpreting Motion

Interpreting Motion How to read a Velocity vs. Time graph

Velocity vs. Time Graphs Constant velocity Constant positive acceleration

Velocity vs.Time graphs Constant negative acceleration but object has changed direction (WHY?) Constant negative acceleration

If you want to know what the average velocity is calculate the slope. Slope = Δv / Δt = aave Δv = vf - vi Δt = tf - ti

Using slope to predict motion • On a velocity vs. time graph • If slope is 0, then acceleration is 0. The velocity is constant. • If slope is positive, acceleration is constant in the positive direction. • If slope is negative, acceleration is constant in the negative direction.

Is the object changing speed? • You must consider both the direction of the velocity and the direction of the acceleration. • If velocity and acceleration are in the same direction object is speeding up. • If the velocity and acceleration are in opposite direction object is slowing down.

Speeding up v Is the velocity positive or negative? +v +a Is the acceleration positive or negative? t -a -v The sign for a and v are the same so both objects are speeding up!

Slowingdown (deceleration) v Is the velocity positive or negative? +v -a Is the acceleration positive or negative? t -v +a The sign for a and v are opposite so both objects are slowing down!

FindingDisplacement • Equal to the “area under the curve” on a v vs. t graph • Triangle A = ½ b×h • Rectangle A = l×w • Base and length are measured in s. • Height and width are measured in m/s. Area = (m/s)(s) = m

V (m/s) Area = l × w length = 3 s width = 50 m/s 50 Δd=150 m 3s ×50 m/s t (s) 1 2 3 4 5 6 7 -25

Velocity vs. Time Graphs • The slope of the line tells you the ____________ of the object. • The “area under the curve” represents the change in position or ____________of an object. displacement acceleration

Interpreting Motion