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Area under a graph Car travelling at 70 mph Area = This is the distance travelled, 140 miles 2 70 = 140 v mph t hours
Car accelerating steadily from 0 to 45 mph in 10 seconds Area = Distance travelled = 110 yards = 110 v mph t seconds mph = = 22 yards per second 22
Car travelling between 2 sets of traffic lights 0 Area of A = t (s) v (ms -1 ) v ms -1 t seconds A A CC B B = 70 Area of C == 17 Area of B = = 13 Total Area = 5 Distance travelled = 70 metres
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.
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
13 Example Find the area under y = 2x 3 - 9x x + 6 between x = 1 and x = 3 y x 0 y = 2x 3 - 9x x + 6 A = + 6x - 3x 3 + 6x 3 -3 1 -3 1 2 = = 22 square units
Distance = The distance travelled is 140 miles = 140 Car travelling at 70 mph v mph t hours Velocity-time graphs v = 70
Car accelerating steadily from 0 to 22 yd/s (45 mph) in 10s v yd/s t seconds gradient = v = 2.2t intercept = 0 = 2.2 Distance = The distance travelled is 110 yards = 110
Car travelling between 2 sets of traffic lights t v v ms -1 t seconds 0 12 Distance travelled = 72 metres v = 0.25t(12 - t) Distance = = 72
Area under a velocity-time graph Car travelling at 70 mph for 2 hours Area = This is the distance travelled, 140 miles 2 70 = 140 v mph t hours
© Nuffield Foundation 2011 Free-Standing Mathematics Activity Speed and distance.
5.1 Accumulated Changes Example 1: An objects travels with a velocity of 15 mph. What is the distance traveled after 4 hours t v Distance = area.
Objectives After completion, you should 1. Know the term displacement, velocity,acceleration and deceleration for motion in a straight line 2. Be familiar.
Speed, Velocity, and Acceleration. Motion What is Motion? Motion is a change in position. Example:
1 of 46© Boardworks Ltd of 46© Boardworks Ltd 2007.
CST W ARM -U P : 10/22/ SLOPE-INTERCEPT FORM OF A LINE.
Motion Recognizing, Describing, and Measuring Motion.
Speed How many measurements for speed can you think of?
Speed and Velocity Speed Velocity Velocity-time graph’s Questions.
Unit Rate $45 for 5 hours. Unit Rate $45 for 5 hours $45 5 H.
Relationship between time, displacement, velocity, acceleration. Kinematic.
1_3 Velocity time graphs Find the area of these shapes. 03 September Find the gradient of these lines yxyx.
Force. Objective Use the equation: net force = mass x acceleration.
25 seconds left….. 24 seconds left….. 23 seconds left…..
Straight Line Motion Looking at position, velocity, and acceleration from the integral.
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.
Aim: How can we calculate average velocity when distance is unknown? Do Now: What is the average velocity between A and B? Velocity (m/s) Time (s)
Distance Time Distance – Time Graph. Distance Time Distance – Time Graph A Click the picture below that matches graph A.
IP2.6.4 Drawing velocity-time graphs © Oxford University Press 2011 Drawing velocity-time graphs.
X = 3y = 4z = 8 2x Step 1X = 3 Step 22(3) 2 – 6 2 Step 4 2(9) – 6 2Step 3 18 – 12 =6.
Average and Constant Acceleration Chapter 2. Acceleration.
1 Speed Learning Objective: To understand and use formulae involving speed. How many units of speed can you think of?
Acceleration Velocity-time graph Questions. Acceleration.
Speed, Velocity and Acceleration What is speed? How is velocity different than speed? What is acceleration? Today’s Goal: Be able to use the proper equations.
STARTER During a road trip, in 6 hours you travel 300 miles. What is your average velocity? Average Velocity = distance travelled/time taken = 300 miles/6.
Motion. Objectives Define motion. Calculate the speed of a moving object. Distinguish between velocity and acceleration.
LESSON 12-1 INVERSE VARIATION Algebra I Ms. Turk Algebra I Ms. Turk.
X and Y Intercepts. The y intercept is the point at which the graph of an equation crosses the y axis. y (0,3)(0,3) x y = 2x + 3.
Physics Physics: The study of forces, motion and energy Motion: Change in position over time compared to a reference point Reference Point: object used.
Acceleration is the rate that velocity changes over time. An object is accelerating if ◦ Its speed changes ◦ Its direction changes ◦ Both its speed.
Around the World AdditionSubtraction MultiplicationDivision AdditionSubtraction MultiplicationDivision.
01. When an object’s distance from another object is changing, it is in ___.
Section 1: Describing Motion. Speed Speed is how far you travel over a period of time. Speed is expressed in the formula s=d/t (speed = distance/time).
Kinetic energy. Equations The kinetic energy of a moving object is one half of the product of its mass multiplied by the square of its velocity. or.
Jeopardy Topic 1Topic Q 1Q 6Q 11Q 16Q 21 Q 2Q 7Q 12Q 17Q 22 Q 3Q 8Q 13Q 18Q 23 Q 4Q 9Q 14Q 19Q 24 Q 5Q 10Q 15Q 20Q 25 Final Jeopardy.
1 Using Kinematic Equations 1. Write down the symbols, values and units (in SI) of given quantities 2. Write down the symbol of the quantities required.
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Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Solving Systems of Linear Equations Graphically and Numerically Basic Concepts.
Distance Time Graphs. Learning Tweet To understand how to plot and read Distance-Time Graphs To understand the relationship between velocity and distance.
P2 – Forces and Motion Lesson 3: D-T and V-T Graphs.
Speed 4 TH GRADE SCIENCE S4P3B. What is speed? Speed is a measurement of how fast an object moves relative to a reference point. It does not have a direction.
Physics: Speed and Velocity Average Speed Rate at which an object moves Units are in distance / time Ex. Meters/second, centimeters/hour.
Motion Which way did it go?. What is Motion? Motion occurs when an object changes position over time.
5 meters in 1 second: 5 m/sec 10 meters in 2 seconds: 5 m/sec 20 meters in 10 seconds: 2 m/sec Biking Speeds:
Section 2.5 Motion with Constant Acceleration © 2015 Pearson Education, Inc.
1.6 – Solving Compound and Absolute Value Inequalities.
Linear Motion. Moving things have two different kinds of motion Linear Motion Harmonic Motion Motion is a change in position in a certain amount of time.
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