Graphical Model of Motion Graphical Model of Motion

Graphical Model of Motion

Graphical Model of Motion • • We will combine our Kinematics Equations with our Graphical Relationships to describe One Dimensional motion! We will be looking at seven graphs!

Graphs for Constant Velocity l l l 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

Displacement vs Time Graph for Constant Velocity l l 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!!

Displacement vs Time Graph for Constant Velocity l l 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.

Velocity vs Time Graph for Constant Velocity l l l 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!

Velocity vs Time Graph for Constant Velocity l l l 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

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

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

Velocity vs Time Graph for Uniform Acceleration l l 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!!

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

Velocity vs Time Graph for Uniform Acceleration l l l 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 (vf +vi)t (starting from rest)

Displacement vs Time Graph for Uniform Acceleration l l 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)

Displacement vs Time Graph for Uniform Acceleration l l l 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 l Similar to d = vit + ½ at 2 (Starting from rest vi = 0) l

Displacement vs Time Squared Graph for Uniform Acceleration l l 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)

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