Motion in a Straight Line

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Presentation transcript:

Motion in a Straight Line

Velocity Velocity - Rate of change of position. Average velocity Instantaneous velocity

How fast? An object moves by the function x(t) = k·t2. What is the speed at t = 2 s? (k = 1m/s2) At t = 0 s, x = 0 m 4.0 At t = 2.0 s, x = 4.0 m 3.0 Position (m) 2.0 1.0 0.5 1.0 1.5 2.0 Time (s)

How fast? (cont.) An object moves by the function x(t) = k·t2. What is the speed at t = 2 s? (k = 1m/s2) At t = 2.0 s, v = 4.0 m/s 4.0 3.0 Position (m) 2.0 1.0 0.5 1.0 1.5 2.0 Time (s)

Acceleration Acceleration - Rate of change of velocity. Average acceleration Instantaneous acceleration

Position, Velocity, & Acceleration 2.0 Position vs. Time 1.0 Position (m) -1.0 -2.0 1.0 2.0 3.0 4.0 5.0 6.0 Time (s) Locate: Zero displacement, zero velocity, & zero acceleration

Kinematic Equation Assumptions Velocity w.r.t. time Average velocity Constant acceleration Initial time is 0s Velocity w.r.t. time Average velocity Position w.r.t. time Velocity w.r.t. position Note: Use the definitions of velocity and acceleration.

Rolling Ball A ball starts at the top of an 8.00 m long ramp with zero initial velocity. It accelerates at a constant rate of 2.00 m/s2. How long does it take for the ball to reach the bottom of the ramp? What is the velocity at the bottom of the ramp?

Earth’s Gravity Near the earth’s surface the acceleration of gravity for an object in free fall is 9.80 m/s2 downward. Ex. A ball is dropped from a roof at a height of 30.0m. How long does it take to hit the ground?

Thrown Ball A ball is thrown over the edge of a cliff with an upward velocity of 8.00 m/s. The cliff is 12.0 m high. How long after the fall is thrown will it ____. Reach max height? Hit the bottom of the cliff? v0

Mass on a Spring The function describing the acceleration of a mass on a spring is What is the function of velocity if the initial velocity is -5.0 m/s?

Stopping a Car A car traveling at 45 mph collides with a tree. The front of the car crumples 1.0 m before it comes to a halt. What is the average acceleration of the car during the collision? v0