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**Chapter 2 Kinematics Slide 1 of 24**

Everything in the universe is in motion. Nothing is permanently at rest. Kinematics These slides adapted from materials from Longman ~ Ismail Brian Wee, 2009 ~ Slide 1 of 24

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**Contents Speed, Velocity and Acceleration Graphical Analysis of Motion**

Free-fall Chapter Review Slide 2 of 24

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Speed Speed, v Speed of an object is defined as the distance travelled per unit time. SI unit of metres per second (ms-1) speed (ms-1) = time taken (s) distance travelled (m) * Note: Remember to USE THE CORRECT UNITS Slide 3 of 24

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Speed Average Speed, v Average speed of an object is defined as the total distance travelled divided by the total time taken. has a unit of metres per second (ms-1) average speed (ms-1) = total time (s) total distance (m) * Note: Remember to USE THE CORRECT UNITS for most journeys, speed is not constant Slide 4 of 24

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**Speed Instantaneous Speed**

Instantaneous speed is the speed of an object at any instant (any point in time). A speedometer measures the instantaneous speed of the car Slide 5 of 24

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**Speed, Velocity and Acceleration**

Velocity, v Velocity is the displacement per unit time in a stated direction; or speed in a specified direction. has a unit of metres per second (ms-1) Velocity (ms-1) = time (s) displacement (m) * Note: Remember to USE THE CORRECT UNITS Slide 6 of 24

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**Speed and Velocity Difference between Speed & Velocity**

scalar quantity vector quantity regardless of its direction dependent on direction of motion A negative velocity indicates that a body is moving in the opposite direction to the direction stated. Slide 7 of 24

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**Velocity Velocity Consider a vehicle travelling around a bend.**

At a road bend, although the vehicle’s speed is constant, its velocity is continuously changing (because direction is constantly changing) Slide 8 of 24

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**Acceleration v – u a = t Acceleration**

Acceleration is defined as the rate of change of velocity. has a unit of metres per second square (ms-2) Acceleration (ms-2) = time taken for the change (s) change of velocity (ms-1) * Note: Remember to USE THE CORRECT UNITS this formula is often used, where v Final Velocity (ms-1) u Initial Velocity (ms-1) t Time taken (s) a = t v – u Slide 9 of 24

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**Acceleration Acceleration**

Uniform acceleration occurs when the velocity increases (or decreases) by the same amount per unit time. [Or rate of change of velocity is constant/uniform] No acceleration (acceleration = 0) Accelerating (positive acceleration) Decelerating (negative acceleration) velocity of the moving object is constant throughout velocity is increasing velocity is decreasing Slide 10 of 24

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**A B Graphical analysis of motion Distance Displacement Displacement**

Distance is the actual or total length travelled by an object in motion. Displacement Displacement is the distance measured along a straight line in a stated direction. A B Displacement Distance Slide 11 of 24

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**Graphical analysis of motion**

Displacement-time graphs Gradient of the displacement-time graph gives the velocity of the object. Displacement / m Displacement / m faster object is not moving slower Time / s Time / s Slide 12 of 24

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**object is moving with constant velocity**

Graphical analysis of motion Displacement-time graphs The displacement-time graph of an object travelling with constant velocity is always a straight line. In a displacement-time graph, the GRADIENT shows the VELOCITY. Thus, Steeper gradient Higher Velocity (faster) Shallower gradient Lower Velocity (slower) Displacement / m faster slower Time / s object is moving with constant velocity Slide 13 of 24

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**Graphical analysis of motion**

Displacement-time graphs Time taken, t/s 10 20 30 40 50 60 70 Distance, x/m 100 200 350 550 850 1200 The instantaneous speed of the car at a particular time can be obtained by finding the slope of the tangent to the graph (gradient) at that point in time. In each successive time interval, 0-10 s, s, and so on, the car covers a greater distance than in the previous one. This means the car is going faster. 550 Slide 14 of 24

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**object has variable velocity**

Graphical analysis of motion Displacement-time graphs Gradient of a tangent to the displacement-time graph of an object travelling with non-uniform velocity gives its instantaneous velocity at a given time. Displacement / m Displacement / m increasing velocity decreasing velocity Time / s Time / s object has variable velocity Slide 15 of 24

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**object moves with constant velocity**

Graphical analysis of motion Velocity-time graphs Gradient of the velocity-time graph gives the acceleration of a moving body. Velocity / ms-1 Velocity / ms-1 object moves with constant velocity object is not moving Time / s Time / s Slide 16 of 24

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**Graphical analysis of motion**

Velocity-time graphs Gradient of the velocity-time graph gives the acceleration of a moving body. Velocity / ms-1 Velocity / ms-1 acceleration deceleration Time / s Time / s object has constant acceleration object has constant deceleration Slide 17 of 24

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**Graphical analysis of motion**

Variable acceleration Gradient of the velocity-time graph gives the acceleration of a moving body. Velocity / ms-1 Velocity / ms-1 increasing acceleration decreasing acceleration Time / s Time / s object has variable acceleration/deceleration Slide 18 of 24

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**Graphical analysis of motion**

Variable acceleration Not all objects move with constant acceleration. Most vehicles move with accelerations that keep changing. The acceleration or deceleration of the object at any point in time is still given by the gradient of the graph at that point. velocity/m s-1 stop stop time/s velocity-time graph of a car on a straight road where it has to stop twice because of traffic lights Slide 19 of 24

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**graphical analysis of motion**

area under a velocity-time graph The area under the velocity-time graph gives the distance travelled by the moving object. Velocity / ms-1 In this example, Distance travelled = area under graph (use square formula) = v t1 uniform velocity v Time / s t1 Slide 20 of 24

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**Graphical analysis of motion**

Area under a velocity-time graph The area under the velocity-time graph gives the distance travelled by the moving object. Velocity / ms-1 In this example, Distance travelled = area under graph (use triangle formula) = ½ v t1 v uniform acceleration Time / s t1 Slide 21 of 24

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**Graphical analysis of motion**

Area under a velocity-time graph The area under the velocity-time graph gives the distance travelled by the moving object. Velocity / ms-1 In this example, uniform velocity Distance travelled = area under graph (use trapezium formula) = ½ ( t1 + t2) v v uniform deceleration Time / s t1 t2 * Note: You can also find the area by adding the area of the square and the area of the triangle Area of trapezium = ½ x (a + b) x height Slide 22 of 24

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**Free fall Acceleration due to gravity**

All objects fall freely towards the centre of the earth and have the same acceleration (acceleration of free fall). all objects fall freely at g 10 ms-2 ( if air resistance is negligible ) speed of a free-falling body increases by 10 ms-1 every second or when a body is thrown up speed of a free-falling body decreases by 10 ms-1 every second or when a body is thrown up Slide 23 of 24

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**Area under velocity-time graph Displacement-time graph represents **

can be plotted as Area under velocity-time graph Displacement-time graph represents Distance Displacement is used to find gives provides can be plotted as represents distance time speed = Gradient of displacement-time graph Velocity-time graph displacement time velocity = average speed = total distance total time is used to find provides represents Gradient of velocity-time graph acceleration = change in velocity time Slide 24 of 24

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