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Graphs & Eqns Motion KW

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Information about Graphs & Eqns Motion KW
Education

Published on May 13, 2010

Author: kwarne

Source: slideshare.net

Description

A set of slides created to teach Graphs & Eqns Motion KW to learners at Bishops Diocesan College in Cape Town.
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Graph Skills The gradient (slope) of a straight line graph is constant and can be found by taking the coordinates between any two points. The gradient of a curve changes continually. At any point the gradient is found by taking the gradient of a tangent to the curve at that point. 1 (x 1 ,y 1 ) 2 (x 2 ;y 2 ) Grad =  y  x y 2 - y 1 x 2 - x 1 = y x 1 (x 1 ,y 1 ) 2 (x 2 ;y 2 ) x 1 y 1 y 2  y  x x Grad at x =  y  x y 2 - y 1 x 2 - x 1 =  y  x

The gradient (slope) of a straight line graph is constant and can be found by taking the coordinates between any two points.

The gradient of a curve changes continually.

At any point the gradient is found by taking the gradient of a tangent to the curve at that point.

SKETCH GRAPHS - Constant Velocity s /(m) t/(s) v/(m/s) t/(s) GRADIENT = velocity AREA = displacement DISPLACEMENT - TIME Graph VELOCITY - TIME Graph The area between any two points on the VELOCITY - TIME graph equals the objects displacement between the two points. t 1 t 2 1 . 2 . The gradient of the DISPLACEMENT vs TIME graph equals the velocity of the object. (at any point) 1 . 2 . ... . . . . . . . . . . . . . . . . . . . . . . . . . .. . .... time/(s) 0 1 2 3 4 5 6 7 8 9 10 1 2 S 1 S 2 s 1 s 2 . . . Displacement increases by same amount in equal time intervals.

SKETCH GRAPHS - Constant ACCELERATION s/(m) t/(s) v (m/s) t/(s) GRAD = a DISPLACEMENT - TIME VELOCITY - TIME t/(s) GRAD = v t 2 t ACCELERATION - TIME a (m/s 2 ) The gradient of the displacement vs time graph (tangent - at any point) gives the velocity of the object at that point. The gradient of the velocity vs time graph (at any point) gives the acceleration of the object. .... . . . . . . . . . . time/(s) 0 1 2 3 4 5 6 7 8 9 10 1 2 S 1 S 2 t 1 s 1 Displacement increases by (uniformly ) increasing amounts in equal time intervals. s 2

-- - - - - - - - - --> CONSTANT ACCELERATION - Summary s/(m) t/(s) v (m/s) t/(s) DISPLACEMENT - TIME VELOCITY - TIME t/(s) t 2 ACCELERATION - TIME a (m/s 2 ) Gradient of the displacement vs time graph gives the velocity . AREA under the VELOCITY vs time graph gives the displacement . AREA of the acceleration vs time graph gives the average velocity . Gradient of the velocity vs time graph gives the acceleration of the object. 1 2 AREA = v AREA = s t 1 1 . 2 . 1 . 2 . t 2 t 1 GRAD = a GRAD = v

Gradient of the displacement vs time graph gives the velocity .

AREA under the VELOCITY vs time graph gives the displacement .

AREA of the acceleration vs time graph gives the average velocity .

Gradient of the velocity vs time graph gives the acceleration of the object.

Graphs Consider the situation when an object is thrown vertically upwards and returns to the throwers hand. Take upwards as positive. Draw the various sketch graphs associated with this particular motion.

Displacement/time Distance/time Velocity/time Speed/time Acceleration/time Vertical motion s t s t v t v t a t + -

Graphs Consider the situation when an object is dropped vertically down, bounces (elastically) and returns to the throwers hand. Take upwards as positive. Draw the various sketch graphs associated with this particular motion.

Displacement/time s t Distance/time Velocity/time Speed/time Acceleration/time Vertical motion s t v t v t a t + -

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