Average speed formula v avg = ½ (vf+vi)

How and when to use the Kinematic Equations v = v0 + at v2 = v02 + 2ad x = v0 t + ½ at2 x = ½ (v + v0) t The acceleration must be constant Draw a diagram if not given List all the givens and what to find Select the equation Plug in givens into correct equation with units substituted Solve with correct units

Applying the kinematic Equations Draw a diagram Choose an appropriate origin Write down the values of the variables Apply the appropriate equations Insert quantities in equations with units Solve for answer with units

The speedboat in the drawing has a constant acceleration of +2.0 m/s2. If the initial velocity of the boat is +6.0 m/s, find its displacement after 8.0 s.

d Given: vi = +30.0 m/s Find: vf = 0 m/s a = –8.00 m/s2 Example 1 Sam approaches a stoplight in her car moving with a velocity of +30.0 m/s. The light turns yellow, Sam applies the brakes and skids to a stop. If Sam’s acceleration is –8.00 m/s2, determine the displacement of the car during the skidding process. Given: vi = +30.0 m/s vf = 0 m/s a = –8.00 m/s2 Find: d

Given: Find: vi = 0 m/s d t = 4.10 s a = 6.00 m/s2 Example 2 Mike is waiting at a stoplight in his car. When the light turns green, Mike accelerates from rest at a rate of 6.00 m/s2 for an interval of 4.10 seconds. Determine the displacement of the car during this time period. Given: vi = 0 m/s t = 4.10 s a = 6.00 m/s2 Find: d

Given: vi = 100 m/s t = 10 s d = 725m Given: vi = 0 m/s t = 4 s Example 3 A plane having an initial velocity of 100 ms-1 covers a displacement of 725 m in 10 s. Find its final velocity. Given: vi = 100 m/s t = 10 s d = 725m Example 4 A dog drops his bone and starts from rest then moves in a straight line with constant acceleration and covers a distance of 64 m in 4 s. What is his acceleration? What is his final velocity? Given: vi = 0 m/s t = 4 s d = 64 m

Given: Given: vi = 10 m/s vi = 20 m/s d = 12 m d = ? vf = 0 vf = 0 Example 5 A truck is initially traveling at 10 m/s and takes 12 meters to stop. If the initial velocity is twice as fast what will be the breaking distance? Given: vi = 10 m/s d = 12 m vf = 0 Given: vi = 20 m/s d = ? vf = 0

Given: vi = 0 m/s t = 4 s a = 1 m/s2 Example 6 A rhinoceros charges from rest and accelerates at 1 m/s2. After 4 seconds what is: Its velocity Its displacement Given: vi = 0 m/s t = 4 s a = 1 m/s2

Example 7 A train starts from rest at a station and accelerates at 2 m/s2 for 10 s. It then runs at constant speed for 30 s, and then slows down at -4 m/s2 until it stops at the next station. What is the distance between the two stations? Part 1 Part 2 Part 3 vi=o a=2 m/s2 t=10s vi= a=0 t=30s a= -4 m/s2 vf =o

Kinematic Equations - Summary