Velocity-Time Graphsand 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-axisa) v(1.0) =

b) v(5.0) =

c) V(11.0) =

What can we determine from a velocity time graph?

• Time (read off the x-axis) a) Time when v = 50

b) Time when v = - 40

a) 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) a(3.0)

b) a (4.0)

c) a (12.0)

d) 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

a) d (first 1.0s)

b) d (first 4.0 s)

c) 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 downOR 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