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 the 1-pound block wins the race. the 100-pound block wins the race. the two blocks end in a tie. 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 the 1-pound block wins the race. the 100-pound block wins the race. the two blocks end in a tie. there’s not enough information to determine which block wins the race. IG2.4

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 x-axis 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 Change in velocity divided by change in time The as at a specific instant of time t is given by the derivative of the velocity

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, 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? (It’s worth including a graphical analysis with this problem.)

Kinematic Curves

Upcoming Assignments MasteringPhysics online HW due tonight by 11 pm Pre-class MasteringPhysics assignment due before class on Tuesday Pre-class MasteringPhysics assignment due before class on Thursday MasteringPhysics online HW due Thursday by 11 pm