Lesson 2 VelocityTime Graphs 1 Example 1 A

Lesson 2: Velocity-Time Graphs 1

Example 1: A car accelerates steadily from rest at 3. 0 m/s 2. Find its velocity at 2, 4, 6, 8, and 10 seconds. Then graph velocity vs. time and find the slope of the graph. a = v – vo t v = vo + at vo = 0 (from rest) v = at v(2 s) = (3. 0 m/s 2) (2 s) v(2 s) = 6. 0 m/s v (m/s) 0 6 12 18 24 30 t (s) 0 2 4 6 8 10

Slope = 12 m/s 4 s Slope = 3. 0 m/s 2 4 24 12 m/s 4 s 8 12 The slope of a velocity-time graph is the acceleration. 3

Try This: Find the acceleration of the object in each time interval (A, B, and C). Describe the motion of the object. A a=2. 5 m/s 2 B a=0 m/s 2 a=-10 m/s 2 C Motion: A = forwards, speeding up; B = forwards at 30 m/s; C = forwards, slowing down, stops at 9 s, then speeds up backwards. 4

Brain Break! 5

Try This: Draw a displacement vs. time graph and a velocity vs. time graph for: a) a car that goes a constant speed, then slows down steadily and stops. b) a bowling ball that is rolled up a ramp and then rolls back down. c) a ball that is dropped and bounces back up to a lesser height. 6

Practice • #3 (c, d, e) and #6 on pg. 52 7

Lesson 3: Calculating Distance from Velocity-Time Graphs 8

Acceleration in the Animal World! 9

Example: Draw a velocity vs. time graph for an object that goes 20 m in 5 s at a constant speed. Find the area between the line and the x-axis. Area = length x width Area = (4 m/s)(5 s) Area = 20 m The area under a velocity-time graph is the displacement! This is true for any velocitytime graph. 10

Try This: An object moves forward at a constant acceleration of 5. 0 m/s 2 for 10 s, starting from rest. How far does it go? (Draw a v vs. t graph. ) Area = ½(base x height) Area = ½(10 s x 50 m/s) Area = 250 m 11

Try This! An object starts at 30 m/s and accelerates at 5. 0 m/s 2 for 10 s. Find the distance it travels. Area = Area of Triangle + Area of Rectangle Area = ½(base x height) + (length x width) Area = ½(10 s x 50 m/s) + (10 s x 30 m/s) Area = 550 m 12

Brain Break! 13

Homework: Complete the Velocity-Time Graphs worksheet. 14