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# Graphs & Equations of Motion

## on May 13, 2010

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A set of slides created to teach Graphs & Equations of Motion to students following the South African National Science curriculum (NSC CAPS) in Cape Town.

A set of slides created to teach Graphs & Equations of Motion to students following the South African National Science curriculum (NSC CAPS) in Cape Town.

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## Graphs & Equations of MotionPresentation Transcript

• SAMPLE ONLY SAMPLE ONLY SAMPLE ONLY For FULL presentation click HERE >> www.warnescience.net Graphs of Motion K Warne
• SAMPLE ONLY SAMPLE ONLY SAMPLE ONLY For FULL presentation click HERE >> www.warnescience.net 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(x1,y1) 2 (x2;y2) Grad = y x y2 - y1 x2 - x1 = y x 1(x1,y1) 2 (x2;y2) x1 y1 y2 y x x Gradat x =y x y2 - y1 x2 - x1 = y x x2
• SAMPLE ONLY SAMPLE ONLY SAMPLE ONLY For FULL presentation click HERE >> www.warnescience.net Constant Velocity Example • Assume you walked for 5s covering 1meter every second. Time (S): 0| 1 | 2 | 3 | 4 | 5 | X (m): 0| 1 | 2 | 3 | 4 | 5 | time (s) Displacement (m) Average Velocity (m/s) Instantaneous Velocity (m/s) Acceleration (m/s2) 0 0 1 1 2 2 3 3 4 4 5 5
• SAMPLE ONLY SAMPLE ONLY SAMPLE ONLY For FULL presentation click HERE >> www.warnescience.net Velocity vs. time • Now calculate the GRADIENT and AREA of this graph. • m = /y/ /x = …/… = … m/s2 • Gradient = …………………….. • AREA = L x b = …. x …. = ….. m (…..)X…. • AREA = ………………………….. v (m/s) t (s) 1 50
• SAMPLE ONLY SAMPLE ONLY SAMPLE ONLY For FULL presentation click HERE >> www.warnescience.net SKETCH GRAPHS - Constant Velocity s/(m) t/(s) v/(m/s) t/(s) GRADIENT = ……….. AREA = ………….. DISPLACEMENT - TIME Graph VELOCITY - TIME Graph The ……………… between any two points on the VELOCITY - TIME graph equals the objects displacement between the two points. t1 t2 1. 2. The ……………………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 S1 S2 s1 s2 . . . Displacement increases by same amount in equal time intervals.
• SAMPLE ONLY SAMPLE ONLY SAMPLE ONLY For FULL presentation click HERE >> www.warnescience.net Constant Acceleration • Assume you started from rest but traveled further every second. Time (S): 0| 1 | 2 | 3 | 4 | 5 | S (m): 0| 0.5| 1.5 | 2.5 | 3.5 | 4.5 | t(s) X (m) Vav Vi a 1 0.5 2 2 3 4.5 4 8 5 12.5 Calculate • aV -Average velocity • Instantaneous velocity • Acceleration
• SAMPLE ONLY SAMPLE ONLY SAMPLE ONLY For FULL presentation click HERE >> www.warnescience.net Constant Acceleration 0 2 4 6 8 10 12 14 0 2 4 6 s 0 1 2 3 4 5 6 0 2 4 6 Vi 0 0.2 0.4 0.6 0.8 1 1.2 0 2 4 6 a Gradient (3.5s) = R/R = (14-0)/(5.8-1.9) = 3.6 m/s = velocity at 3.5s Gradient = R/R = 6/6 = 1.0 m/s2 = acceleration Area = l x b = 5 x 1 = 5 m/s = change in velocity!
• SAMPLE ONLY SAMPLE ONLY SAMPLE ONLY For FULL presentation click HERE >> www.warnescience.net SKETCH GRAPHS - Constant ACCELERATION s/(m) t/(s) v (m/s) t/(s) GRAD = …. DISPLACEMENT - TIME VELOCITY - TIME t/(s) GRAD = … t2 t ACCELERATION - TIME a (m/s2) The gradient of the displacement vs time graph (tangent - at any point) gives the ……………..of the object at that point. The gradient of the velocity vs time graph (at any point) gives the ……………….of the object. .... . . . . . . . . . . time/(s) 0 1 2 3 4 5 6 7 8 9 10 1 2 S1 S2 t1 s1 Displacement increases by (uniformly ) increasing amounts in equal time intervals. s2
• SAMPLE ONLY SAMPLE ONLY SAMPLE ONLY For FULL presentation click HERE >> www.warnescience.net . Graphs of Motion A - acceleration (+) B - constant velocity (+) C - deceleration (+) D - stationary E - reverse acceleration (-) F - reverse constant v (-) G - reverse deceleration (-) t t t s a A B C D E F G v ... . . . . . . . . . . . . . . . . . . . . . . ... . . . . . .. . . . . . . . . . ... . . . . . . .
• SAMPLE ONLY SAMPLE ONLY SAMPLE ONLY For FULL presentation click HERE >> www.warnescience.net . ........................................ . . . . . . . . SKETCH GRAPHS - Displacement vs Time s/(m) t/(s) Constant Velocity Displacement changes by same amount every second. s/(m) t/(s) Constant Acceleration Increasing displacement per second - velocity increases. s (m) t/(s) Stationery Object Displacement remains constant. Displacement is being reduced (coming back to start). s (m) t/(s) Object moves backwards. ............................ s (m) t/(s) Deceleration. Rate of increase in displacement decreases - slowing down. . . . . ....
• SAMPLE ONLY SAMPLE ONLY SAMPLE ONLY For FULL presentation click HERE >> www.warnescience.net SKETCH GRAPHS - Task s/(m) t/(s) v/(m/s) t/(s) Draw sketch graphs of displacement vs time, velocity vs time and acceleration vs time for a car that starts off from rest, accelerates uniformly for 5s, attains a speed of 30m/s which it maintains for 10s. The car then slows down for 15s at which point it comes to a halt. Indicate as much detail on the graphs as possible. a/(m/s2) t/(s)
• SAMPLE ONLY SAMPLE ONLY SAMPLE ONLY For FULL presentation click HERE >> www.warnescience.net SKETCH GRAPHS - Example Tut on Graphs & equations 0 10 20 30 40 8 12 |
• SAMPLE ONLY SAMPLE ONLY SAMPLE ONLY For FULL presentation click HERE >> www.warnescience.net Tut on Graphs & equations 0 10 20 30 40 8 -12 | constant velocity slowing down (decelerating uniformly) speeding up reverse uniform acceleration negative direction slowing (decelerating) down backwards constant velocity accelerating forwards constant velocity V
• SAMPLE ONLY SAMPLE ONLY SAMPLE ONLY For FULL presentation click HERE >> www.warnescience.net Graphs of two motions. The graph shows the speeds of two cars A & B as a function of time. 1. What is the difference in the distances traveled by A & B after 20 s? (7) 2. After how many seconds will A & B have traveled the same distance? (6) 3. Calculate the acceleration of A. (4) B A 1510 5 6 v t (s) 20
• SAMPLE ONLY SAMPLE ONLY SAMPLE ONLY For FULL presentation click HERE >> www.warnescience.net Graphs of Vertical Motion An object is thrown vertically up and returns to the thrower’s hand. 0 10 20 30 V (m/s) 0 -10 -20 -30 0 -10 -20 -30 30 20 10 X t t t V a
• SAMPLE ONLY SAMPLE ONLY SAMPLE ONLY For FULL presentation click HERE >> www.warnescience.net Hi - This is a SAMPLE presentation only. My FULL presentations, which contain a lot more more slides and other resources, are freely available on my resource sharing website: www.warnescience.net (click on link or logo) Have a look and enjoy! WarneScience