kinematics in one dimension: part ii - siena college · kinematics in one dimension: part ii...
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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)
Upcoming Assignments
• MasteringPhysics online HW due tonight by 11 pm
• Read all of Chapter 3 by Tuesday 9/18 • Pre-class MasteringPhysics assignment due before
class on Tuesday 9/18 • Pre-class MasteringPhysics assignment due before
class on Thursday 9/20
• MasteringPhysics online HW due Thursday 9/20 by 11 pm
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