Download presentation

Presentation is loading. Please wait.

Published byAlaina Keal Modified over 2 years ago

1
Area under a graph Car travelling at 70 mph Area = This is the distance travelled, 140 miles 2 70 = 140 v mph t hours 0 2 70

2
Car accelerating steadily from 0 to 45 mph in 10 seconds Area = Distance travelled = 110 yards = 110 v mph t seconds 0 10 45 45 mph = = 22 yards per second 22

3
Car travelling between 2 sets of traffic lights 0 Area of A = t (s) v (ms -1 ) 0 0 2 5 4 8 8 8 10 5 12 0 6 9 v ms -1 t seconds 12 624810 A A CC B B = 70 Area of C == 17 Area of B = = 13 Total Area = 5 Distance travelled = 70 metres

4
y x 0 a b Integration As x 0 Integration is the inverse of differentiation. lim x 0 A = As A = y x A = xx y y x AA The gradient of the graph of A against x.

5
Rules of Integration = x y = 5x = 5 y = c = 0 Function Derivative Reverse to give integral = 5x y = = x 2 y = = x 3 y = + c

6
13 Example Find the area under y = 2x 3 - 9x 2 + 12x + 6 between x = 1 and x = 3 y x 0 y = 2x 3 - 9x 2 + 12x + 6 A = + 6x - 3x 3 + 6x 2 + 6 3 -3 3 3 + 6 3 2 + 6 1 -3 1 3 + 6 1 2 = 31.5- 9.5 = 22 square units

7
Distance = The distance travelled is 140 miles = 140 Car travelling at 70 mph v mph t hours 0 2 70 Velocity-time graphs v = 70

8
Car accelerating steadily from 0 to 22 yd/s (45 mph) in 10s v yd/s t seconds 0 10 22 gradient = v = 2.2t intercept = 0 = 2.2 Distance = The distance travelled is 110 yards = 110

9
Car travelling between 2 sets of traffic lights t024810126 v0588509 v ms -1 t seconds 0 12 Distance travelled = 72 metres v = 0.25t(12 - t) Distance = = 72

Similar presentations

OK

Warm-up - 9/22/16 1)A supersonic jet travels around the Earth once at an average speed of 1.6 x 10 3 km/hr a distance of 4.1 x 10 4 km. How many hours.

Warm-up - 9/22/16 1)A supersonic jet travels around the Earth once at an average speed of 1.6 x 10 3 km/hr a distance of 4.1 x 10 4 km. How many hours.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Design ppt online Ppt on careers in science Ppt on time division switching pdf Ppt on low level language and high level Ppt on structure of human respiratory system Ppt on historical and heritage site tourism Ppt on india political history Ppt on economic growth and development Ppt on great indian mathematicians Ppt on different model of atom