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 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 •  The time rate of change of

velocity

•  Change in velocity divided by change in time

Instantaneous Acceleration •  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?

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