Velocity-Time Graphs and Acceleration

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Presentation transcript:

Velocity-Time Graphs and Acceleration

What does a v-t graph look like? Time is marked on the horizontal axis and velocity is on the vertical. Graphs that represent an object’s velocity versus its time.

What can we determine from a velocity time graph? Velocity and speed Time Acceleration Displacement and distance

What can we determine from a velocity time graph? Velocity - reading directly off the y-axis v(1.0) = v(5.0) = V(11.0) =

What can we determine from a velocity time graph? Time (read off the x-axis) Time when v = 50 b) Time when v = - 40 Time when v = 0

What can you find from a v-t graph Instantaneous Acceleration = slope at a point on the graph (you may have to use a tangent) Average acceleration = finding the slope of a segment (use the start and end points)

What can we determine from a velocity time graph? Acceleration = v/t = slope a(3.0) b) a (4.0) a (12.0) a (ave for first 11.0 s)

What can we determine from a velocity time graph? Displacement = area under the curve NOTE: Area formulas: Arearectangle = length x width Areatriangle = ½ base x height d (first 1.0s) b) d (first 4.0 s) a (entire trip)

Velocity-Time Graphs

Interpreting v-t graphs Horizontal lines show uniform motion (constant speed and direction). Inclined lines show change in speed or direction, or both: in other words accelerated motion.

Summary Slide: Velocity-Time Graphs Independent Variable = Dependent Variable = Above x-axis = Below x-axis = On x-axis = Linear sections

Summary Slide: Velocity-Time Graphs Slope = + slope (2 scenarios)= - slope (2 scenarios) = Horizontal Line Average acceleration: Instantaneous acceleration:

Summary Slide: Velocity-Time Graphs Steeper slope means _______________________ To find velocity: read off ______ at a point To find displacement: Find time: read off the ------------------- at a point

Summary Slide: Velocity-Time Graphs Independent Variable = time Dependent Variable = velocity Above x-axis = moving forward (positive v) Below x-axis = moving backward (negative v) On x-axis = stationary (v = 0) Linear sections = constant acceleration

Summary Slide: Velocity-Time Graphs Slope = acceleration + slope (2 scenarios)= moving forward, speeding up OR moving backward, slowing down - slope (2 scenarios) = moving forward, slowing down OR moving backward, speeding up Horizontal Line = no acceleration (slope = 0) Average acceleration: draw a line from start to end and find its slope Instantaneous acceleration: slope at a point (use tangent)

Summary Slide: Velocity-Time Graphs Steeper slope means speeding up or slowing down quickly (changing speed quickly – like hitting the brakes rather than putting the brakes on 10m before stop sign) To find velocity: read off y-axis at a point To find displacement: area between curve and x-axis (find total area of rectangles and triangles) Find time: read off the x-axis at a point