Kinematics in One Dimension: Part II

Constant Acceleration

•  Many applications (e.g., free-fall) •  Kinematic equations

Graphical representation of acceleration, velocity, and position (and vice versa)

Integrate acceleration vs time graph to find velocity

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

a =�v

�t

Constant Velocity vs Constant Acceleration

Trajectory of a ball

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

Motion with Constant Acceleration

Problem-Solving Strategy: Kinematics with constant acceleration

A ball rolls up the ramp, then back down. Which is the correct acceleration graph?

Think-Pair-Share

QuickCheck 2.19 Think-Pair-Share

A ball rolls up the ramp, then back down. Which is the correct acceleration graph?

A worked example

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?

Another worked example

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?

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

Recap: Interpreting graphical representations of motion

Kinematic Curves Worksheet

•  Do the odd-numbered curves individually •  Front: Find velocity, acceleration given position •  Back: Find position, acceleration given velocity

•  If you are done early, do the even ones, too! •  Group whiteboard and share 1-2 hard ones at

the end •  Finish the rest at home (will not be graded)

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class on Tuesday 9/18 •  Pre-class MasteringPhysics assignment due before

class on Thursday 9/20

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