5 Average speed formula v avg vfvi 1

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

1) The acceleration must be constant v = v 0 + at 2) Draw a diagram if not given v 2 = v 02 + 2 ad 3) List all the givens and what to find x = v 0 t + ½ at 2 4) Select the equation x = ½ (v + v 0) t 5) Plug in givens into correct equation with units substituted 6) Solve with correct units

Applying the kinematic Equations ØDraw a diagram ØChoose an appropriate origin ØWrite down the values of the variables ØApply the appropriate equations ØInsert quantities in equations with units ØSolve for answer with units

The speedboat in the drawing has a constant acceleration of +2. 0 m/s 2. If the initial velocity of the boat is +6. 0 m/s, find its displacement after 8. 0 s.

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/s 2, determine the displacement of the car during the skidding process. Given: vi = +30. 0 m/s vf = 0 m/s a = – 8. 00 m/s 2 Find: d

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/s 2 for an interval of 4. 10 seconds. Determine the displacement of the car during this time period. Given: Find: vi = 0 m/s d t = 4. 10 s a = 6. 00 m/s 2

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 Example 4 d = 725 m A dog drops his bone and starts from rest then moves in a straight line with constant acceleration and covers a distance Given: of 64 m in 4 s. a. What is his acceleration? vi = 0 m/s b. What is his final velocity? t=4 s d = 64 m

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 vi = 20 m/s d = 12 m d=? vf = 0

Example 6 A rhinoceros charges from rest and accelerates at 1 m/s 2. After 4 seconds what is: a. Its velocity b. Its displacement Given: vi = 0 m/s t=4 s a = 1 m/s 2

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

Kinematic Equations - Summary