ACCELERATION AND VELOCITY



DISPLACEMENT FROM VELOCITY-TIME GRAPHS

Recall…

When given a speed-time graph, the total distance traveled is represented by the ______ under the line

On a velocity-time graph, the area under the line (ie. between the line and the ________ axis) represents the __________________________ during the time interval covered by the line

EXAMPLE 1A

Using the velocity-time graph, calculate the resultant displacement of the dragonfly

EXAMPLE 1B

Using the velocity-time graph, calculate the displacement of the car

DISPLACEMENT DURING CONSTANT ACCELERATION

Horse A _____________ from an ______________ ([pic]) to a __________________ ([pic])

[pic]

Horse B is traveling at a _____________, which is the __________ of [pic] and [pic]

( Horse B’s velocity is equal to the ___________ between Horse A’s [pic] and [pic]

If acceleration is constant, we can calculate displacement by using the formula:

The other variables can be solved for using algebraic methods.

EXAMPLE 2

If Horse A (from the figure on the previous page) accelerates constantly from 6.0 m/s [E] to 16.0 m/s [E] in a time of 7.4 s, what is the displacement of the horse? Assume east [E] is positive.

EXAMPLE 3

A grasshopper is displaced 0.040 m [up] while extending its legs at the beginning of a jump. It accelerates positively from 0 to 3.4 m/s [up]. Assume constant acceleration, calculate how long this takes. Assume that up is positive.

FINDING DISPLACEMENT WHEN FINAL VELOCITY IS NOT GIVEN

When final velocity is not known but other quantities are known, the formula to be used is:

If [pic], then the formula is simply

Like other formulas, algebraic methods can be used to solve for the other variables

EXAMPLE 4

A kangaroo leaves the ground with an initial velocity of 7.0 m/s [up] and an acceleration of 9.81 m/s2 [DOWN]. The kangaroo reaches its max. height in 0.71 s. What is the displacement/height at the top of the jump? Assign up as positive.

EXAMPLE 5

A speedboat accelerates constantly from rest at 2.1 m/s2 [S] for a displacement of 70.0 m [S]. How long did this acceleration last? Assign south as positive.

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