Think Pair Share 1 A 1 pound block

Think – Pair - Share 1. A 1 -pound block and a 100 -pound block are placed side by side at the top of a frictionless hill. Each is given a very light tap to begin their race to the bottom of the hill. In the absence of air resistance A. the 1 -pound block wins the race. B. the 100 -pound block wins the race. C. the two blocks end in a tie. D. there’s not enough information to determine which block wins the race.

A 1 -pound block and a 100 -pound block are placed side by side at the top of a frictionless hill. Each is given a very light tap to begin their race to the bottom of the hill. In the absence of air resistance A. the 1 -pound block wins the race. B. the 100 -pound block wins the race. C. the two blocks end in a tie. D. there’s not enough information to determine which block wins the race.

Position-Versus-Time • Trucker Bob starts the day 120 miles west of Denver. He drives east for 3 hours at a steady 60 miles/hour before stopping for his coffee break. • Draw a position-versus-time graph for Bob, including appropriate numerical scales along both axes. • Let Denver be located at x = 0 and assume that the xaxis points to the east.

Uniform Motion Straight-line motion in which equal displacements occur during any successive equal-time intervals is called uniform motion. For one-dimensional motion, average velocity is given by Notice the symbol Δ. It represents a displacement and an interval in time - not position or instant in time

Problem Solving Strategy • Sally opens her parachute at an altitude of 1500 m. She then descends slowly to earth at a steady speed of 5 m/s. How long does it take her to touch down? • Draw pictorial representation – coordinates, symbols • Motion diagram • Mathematical Representation • Are results reasonable?

Acceleration Average Acceleration Instantaneous Acceleration • The time rate of change of velocity • The as at a specific instant of time t is given by the derivative of the velocity • Change in velocity divided by change in time

Trajectory of a ball Turning point – What is the acceleration as the ball rises, drops, at the top?

Tactics: Interpreting graphical representations of motion

Motion with Constant Acceleration

Finding Velocity from the Acceleration If we know the initial velocity, vis, and the instantaneous acceleration, as a function of time, t, then the final velocity is given by Or, graphically,

EXAMPLE 2. 21 Finding velocity from acceleration QUESTION:

EXAMPLE 2. 21 Finding velocity from acceleration

Problem-Solving Strategy: Kinematics with constant acceleration

Example 1 Bob throws a ball straight up at 20 m/s, releasing the ball 1. 5 m above the ground. What is the maximum height of the ball? What is the ball’s impact speed as it hits the ground?

Example 2 A sprinter accelerates at 2. 5 (m/s)/s until reaching his top speed of 15 m/s. He then continues to run at top speed. How long does it take him to run the 100 -m dash?

Kinematic Curves

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