I.A.1 – Kinematics: Motion in One Dimension

Average velocity, constant acceleration and the “Big Four”

Ex. An object with an initial velocity of 4.0 m/s moves along a straight line under constant acceleration. After a time of 3.0 s, its velocity is 14 m/s. How far did it travel during this time?

Ex. A car initially traveling at 10.0 m/s accelerates uniformly at a rate of 2.0 m/s 2 for a time of 4.0 s. How far does the car travel during this time?

Ex. A rock is dropped from a cliff that is 80.0 m high. What is the final velocity of the rock as it hits the ground?

Ex. A severed foot is thrown upward with an initial speed of 20.0 m/s. What will be the maximum height (above the point at which it was thrown) of the foot?

Ex. A cell phone is thrown straight down with a speed of 20.0 m/s. How fast will the cell phone be moving 2.0 s after it was thrown?

Ex. A graduation cap is thrown straight upward with a speed of 8.0 m/s and strikes the ground 3.0 s later. From what height was the cap thrown? Air resistance is negligible.

p. 47: 52, 54, 58-59, m 54. v = 3 m/st = 0.5 s m 59. a) -5.1 EE 5 m/s 2 b) 6.9 EE -4 s m

A note on signs: if velocity and acceleration have the same sign, the object is increasing in speed. If velocity and acceleration have opposite signs, the object is decreasing in speed.

Position vs. time graphs – the slope of a position vs. time graph is velocity.

Velocity vs. time graphs – the slope of a velocity vs. time graph is acceleration. The area under a curve for velocity vs. time is displacement.

Practice Graphs

Ex. A baseball is tossed vertically with an initial velocity of 12 m/s. a) How long does it take the ball to reach maximum height? b) What is the maximum height above the release point? c) How long does it take the ball to reach a point 5.0 m above the release point?

p. 47: 55, 57, 65-66, m 57. a) 4.1 sb) 20 mc) 1 s, 3 s m 66. a) -26 mb) 23 m/s 73. a) mb) 138 sc) -610 m/s