2020 - Day 8 - Velocity-Time Graphs & Acceleration - Presentation
Page 1: Velocity-Time Graphs and Acceleration
Velocity: the rate of change of position (displacement).
Found as the slope on a displacement-time graph.
Acceleration: the rate of change of velocity.
Determined by the slope on a velocity-time graph.
Acceleration can be defined as the change in velocity over time.
When an object slows down, its acceleration is opposite to its velocity (deceleration) and has a negative value.
Constant Acceleration: Equal to the slope of a straight line on the velocity-time graph.
Formula: ( a = \frac{\Delta V}{\Delta t} = \frac{V_2 - V_1}{t_2 - t_1} )
Page 2: Sample Problems
Sample Problem 1: Analyze the acceleration for different intervals:
For 0-10 s:
( a_{10s} = \frac{V_{10s} - V_{0s}}{10s - 0s} = \frac{2 m - 0 m}{10 s} = 0.2 m/s^2 )
For 10-15 s:
( a_{10-15s} = \frac{V_{15s} - V_{10s}}{15s - 10s} = \frac{3 m - 2 m}{5 s} = 0.2 m/s^2 )
For 15-20 s:
( a_{15-20s} = \frac{V_{20s} - V_{15s}}{20s - 15s} = \frac{6 m - 3 m}{5 s} = 0.6 m/s^2 )
Page 3: Calculating Accelerations
Task: Calculate acceleration in different segments of the graph:
Each section labeled A, B, C, D, and E corresponds to a specific acceleration segment.
These calculations are based on the slope of the graph between the points defined by the sections.
Page 4: Acceleration Analysis
Calculations for graph segments:
A: ( a_A = \frac{0 m - 0 m}{2s - 0s} = 0)
B: Increase from 1 m to 7 m over 6 s gives:
( a_B = \frac{7 m - 1 m}{6s - 2s} = 1.5 m/s^2 )
C: The value remains constant from 1 m to 0 m:
( a_C = \frac{0 m - 1 m}{7s - 6s} = -1 m/s^2 )
D: More complex, calculated similarly.
E: Positive acceleration leads up to a braking phase.
Page 5: Mouse Movement Analysis
Analyze the mouse's motion through questions:
(a) When is the mouse stationary?
(b) Identify intervals of constant velocity.
(c-g) Calculations regarding acceleration, including maximum and minimum values during given intervals.
Page 6: Continuing Motion Analysis
Further assessments of acceleration during intervals with specified questions regarding values and conditions for motion.
Page 7: Motorcycle Motion Analysis
Analyze motorcycle's velocity in a similar manner:
(a) Constant velocity intervals.
(b-c) Determine maximum velocities in both directions.
(d-f): Maximum and minimum accelerations calculated.
Page 8: Continued Motorcycle Acceleration Analysis
Follow up calculations from previous observations regarding accelerations over specified time intervals to understand motion behavior.
Page 9: Instantaneous Acceleration
Understanding instantaneous acceleration through tangent slopes at specific points on the graph.
Average acceleration can be deduced by secant slope between two distinct points.
Page 10: Practice Problems - Example 1
Given a new velocity-time graph for practice, determine the following:
(i) Identify constant velocity segments.
(ii-iv) Acceleration values during respective segments.
Page 11: Continued Practice Problems
Calculation examples follow-up from previous findings for segments BC, FG, and average values.
Page 12: Velocity-Time Graph Review
A second example with a new graph demands detailed acceleration analyses.
Page 13: Further Detailed Acceleration Analysis
Specific calculations requested for segments HI, BG, and situations when the acceleration equals zero.
Page 14: Example 3: Detailed Acceleration Analysis
Analyze another graph to identify segments with zero and uniform acceleration; demonstrate calculations.
Page 15: Final Thoughts on Graphs
Understanding the significance of the slope of the line AD representing the average velocity over a time interval.