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1. A coordinate system provides a systematic means of specifying the position of a particle. A system in one dimension involves choosing an origin and a positive direction in which values of the position coordinate increase. Values of the position coordinate are positive or negative numbers multiplied by an appropriate unit of length, usually the SI unit of length, the metre (m).

2. The movement of a particle along a line can be described graphically by plotting values of the particle’s position *x*, against the corresponding times *t*, to produce a position-time graph. Alternatively, by choosing an appropriate reference position *x*_{ref}and defining the displacement from that point by *s _{x}* =

3. Uniform motion along a line is characterised by a straight-line position-time graph that may be described by the equation

where *v*_{x} and *x*_{0} are constants. Physically, *v*_{x} represents the particle’s velocity, the rate of change of its position with respect to time, and is determined by the gradient of the position-time graph

*x*_{0} represents the particle’s initial position, its position at *t* = 0, and is determined by the intercept of the position-time graph, the value of *x* at which the plotted line crosses the *x*-axis, provided that axis has been drawn through *t* = 0.

4. Non-uniform motion along a line is characterised by a position-time graph that is not a straight line. In such circumstances the rate of change of position with respect to time may vary from moment to moment and defines the instantaneous velocity. Its value at any particular time is determined by the gradient of the tangent to the position-time graph at that time.

5. More generally, if the position of a particle varies with time in the way described by a function *x*(*t*), then the way in which the (instantaneous) velocity varies with time will be described by the associated derived function or derivative

6. The instantaneous acceleration is the rate of change of the instantaneous velocity with respect to time. Its value at any time is determined by the gradient of the tangent to the velocity-time graph at that time. More generally, the way in which the (instantaneous) acceleration varies with time will be described by the derivative of the function that describes the instantaneous velocity, or, equivalently, the second derivative of the function that describes the position:

7. Results and rules relating to differentiation and the determination of derivatives are contained in Table 6. The derivative of a constant is zero, the derivative of *f*(*y*) = *Ay ^{n}* is d

8. The signed area under a velocity-time graph, between specified values of time, represents the change in position of the particle during that interval.

9. Uniformly accelerated motion is a special case of non-uniform motion characterised by a constant value of the acceleration, *a _{x}* = constant. In such circumstances the velocity is a linear function of time (

10. The most widely used equations describing uniformly accelerated motion are

11. Position *x*, displacement *s _{x}*, velocity

1. The most widely used equations describing uniformly accelerated motion in a straight line along a horizontal surface, which is taken as along the x-axis are:

Note: Position *x*, displacement *s _{x}*, velocity

For example, an object travelling at 10 m/s East, its initial velocity, *u* _{x } = +10 m/s as its direction, East is taken as the positive direction. After 2 seconds, this object then traveled at 30 m/s West, its final velocity will be taken as, *v* _{x} = – 30 m/s, as its direction, West is taken as the negative direction.

2. Another most widely used equations describing uniformly accelerated motion in a straight line of an object thrown upwards or dropped downwards perpendicular to the surface, which is taken as along the y-axis are:

Note: Position y, displacement *s y*, velocity *v* _{y }, and acceleration, *a _{y}*, are all signed quantities that may be positive or negative, depending on the associated direction.

For example, an object travelling 10 m/s downwards, its initial velocity, *u* _{x } = -10 m/s as its direction, downward direction is taken as the negative direction. After 2 seconds, this object then traveled at 30 m/s downwards, its final velocity will be taken as, *v* _{x} = -30 m/s, as its direction, downwards is taken as the negative direction.

The magnitude of the acceleration due to gravity is represented by the symbol *g*, and if it has a value 9.8 m s^{−2} (in the formula sheet near the Earth surface). Since the downward direction is negative, then the acceleration due to gravity = – 9.8 m s^{−2 }

Accelerators and liquids in cans

4×4 competitions

Problem to solve: How to transport liquids in the container (can ) without spilling?

In small groups:

(1) discuss the different ways you can secure the can in your effort to minimise the loss of liquid in the can (the load )

(2) design simple experiments you can do to observe the movement of liquids in the clear plastic bottle at different speeds or angles

(3) do the experiments and write up your observations in your blog.

Lesson 7th March

UAV Performance Test

Download the file below:

Analysing forces – force diagram worksheet

adapted from:

Year 9

Topic Waves Quiz 1 Longitudinal and Transverse wave at this link using email account or google accound. Just simply type in the code: 56cccf