1. Graphical Model of Motion

2. We will combine our Kinematics Equations with our Graphical Relationships to describe One Dimensional motion! We will be looking at seven graphs!

3. Graphs for Constant Velocity Velocity = constant (Acceleration = 0) v = d/t From the equation v = d/t, make a data table with t, d, v, a. – Time is the independent variable

4. Displacement vs Time Graph for Constant Velocity d vs t is linear – y = mx +b Slope (m) from a d vs t graph is always, Velocity! Since graph is linear, slope (m) is Constant! Therefore: Velocity is Constant!!

5. Displacement vs Time Graph for Constant Velocity The y-intercept (b) = Where you are starting from when t=0! Graphing a Complete trip! – Every graph tells a story! – Time keeps going even when you are not! – We can find the Instantaneous Velocity, Average Speed and Average Velocity.

6. Velocity vs Time Graph for Constant Velocity Since the Velocity is constant, the graph is a horizontal line (Constant Relationship) Slope of a velocity vs time graph is always acceleration! Since the slope of a horizontal line is zero and the slope is the acceleration, Therefore: acceleration = 0!

7. Velocity vs Time Graph for Constant Velocity We can find the displacement from a velocity vs time graph by finding the Area Under the Curve! d = Area under the Curve Area will be a rectangle: – A = l x w = displacement

8. Acceleration vs Time Graph for Constant Velocity Since the acceleration = zero the graph is a horizontal line on the x-axis (a = 0). We cannot find anything from this graph!

9. Uniform Acceleration Graphs Acceleration (a) is constant. Make a Data Table with your Kinematics Equations Looking a four graphs.

10. Velocity vs Time Graph for Uniform Acceleration v vs t is linear – y = mx +b Slope (m) from a v vs t graph is always, Acceleration! Since graph is linear, slope (m) is Constant! Therefore: Acceleration is Constant!!

11. Velocity vs Time Graph for Uniform Acceleration The y-intercept (b) = Your Initial Velocity (v i ). The speed you are starting with when t=0! y = mx + b becomes; v = at + v i similar to v f = v i + at

12. Velocity vs Time Graph for Uniform Acceleration We can find the displacement from a velocity vs time graph by finding the Area Under the Curve! d = Area under the Curve Area will now be a triangle: – A = ½ b x h = displacement – Similar to d = ½ (v f +v i )t (starting from rest)

13. Displacement vs Time Graph for Uniform Acceleration d vs t is parabolic – y = kx 2 Slope (m) from a d vs t graph is Velocity! Since graph is parabolic, the slope is Not Constant! Therefore: Velocity is Not Constant! (The object is accelerating)

14. Displacement vs Time Graph for Uniform Acceleration d vs t is parabolic, y = kx 2 Unit for the constant (k) is m/s 2 k = half the acceleration (1/2 a) y = kx 2 becomes; d = ½ at 2 Similar to d = v i t + ½ at 2 (Starting from rest v i = 0)

15. Displacement vs Time Squared Graph for Uniform Acceleration Squaring the Time will straighten out the parabola and make the graph linear. d vs t 2 is linear – y = mx +b Slope (m) from a d vs t 2 graph is half the acceleration (1/2 a) Since graph is linear, slope (m) is Constant! (The acceleration is still constant)

16. Acceleration vs Time Graph for Uniform Acceleration Since the Acceleration is constant, the graph is a horizontal line (Constant Relationship) We can find the change in velocity (  v) from an acceleration vs time graph by finding the Area Under the Curve!  v = Area under the Curve Area will be a rectangle: – A = l x w = change in velocity (  v)