DO NOW Superman is looking for Lois Lane. He starts flying from the roof of the Daily Planet, flies 5km east, 5 km north, 5 km south and 7 km west. He took 2 hours to complete the journey – What was his displacement? – What was his distance? – What was his Speed? – What was his velocity?

After today WE will be able to: 1) Describe characteristics of a Displacement vs. Time Graph 2) Calculate the displacement, distance, speed, and velocity of an object in a Displacement vs. Time Graph 3) Calculate displacement given a Velocity vs. Time Graph

Displacement vs. Time Quiz 1)From the graph above, identify which segment of the graph is not moving 2)Identify which segment of the graph (A,B,C) is going the slowest

Displacement vs. Time Quiz 3)Which segment of the graph (A,B,C) is going the fastest? 4)Which segment of the graph is showing the object move backwards

Displacement vs. Time Quiz 5)Which segment moves forward 6)What is the distance covered by the object?

Displacement vs. Time Quiz 7)What is the displacement of the object? 8)What is the speed of the object?

Displacement vs. Time Quiz 1)What is the velocity of the object? 1)Solve for x: 78x – 4 = 92 (round to the nearest hundredth)

All 3 Graphs t x v t a t

Graphing Tips 1) Line up the graphs vertically. 2) Draw vertical dashed lines at special points except intercepts. 3) Map the slopes of the position graph onto the velocity graph. 4) A red peak or valley means a blue time intercept. t x v t

Graphing Tips The same rules apply in making an acceleration graph from a velocity graph. Just graph the slopes! Note: a positive constant slope in blue means a positive constant green segment. The steeper the blue slope, the farther the green segment is from the time axis. a t v t

Real life Note how the v graph is pointy and the a graph skips. In real life, the blue points would be smooth curves and the green segments would be connected. In our class, however, we’ll mainly deal with constant acceleration. a t v t

Area under a velocity graph v t “ forward area” “backward area” Area above the time axis = forward (positive) displacement. Area below the time axis = backward (negative) displacement. Net area (above - below) = net displacement. Total area (above + below) = total distance traveled.

Area The areas above and below are about equal, so even though a significant distance may have been covered, the displacement is about zero, meaning the stopping point was near the starting point. The position graph shows this too. v t “forward area” “backward area” t x

Area units Imagine approximating the area under the curve with very thin rectangles. Each has area of height  width. The height is in m/s; width is in seconds. Therefore, area is in meters! v (m/s) t (s) 12 m/s 0.5 s 12 The rectangles under the time axis have negative heights, corresponding to negative displacement.

Graphs of a ball thrown straight up x v a The ball is thrown from the ground, and it lands on a ledge. The position graph is parabolic. The ball peaks at the parabola’s vertex. The v graph has a slope of -9.8 m/s 2. Map out the slopes! There is more “positive area” than negative on the v graph. t t t

Velocity (m/s) Example!!

Velocity (m/s) DOL: Calculate the Displacement Under the Curve