 It is really important that you use the right words in the right context, especially in definitions  Use units to define units and quantities to define quantities  Eg – acceleration is the change in velocity per unit time NOT the change in velocity per second

 Displacement is the vector quantity of distance.  It has a stated direction  Can be stated as an angle, bearing or from a reference point

 Velocity is the vector quantity of speed  It has a stated direction  Can be stated as an angle, bearing or from a reference point  Velocity can be defined as the rate of change of distance in a given direction.  v = d/t

 Acceleration is defined as the rate of change of velocity  It has a stated direction but a negative acceleration IS NOT called deceleration. It’s just a negative acceleration.  Can be stated as an angle, bearing or from a reference point  a = (v-u)/t  v = u + at

Displacement-Time graphs These contain lots of information about the type of motion a body is experiencing as discovered at GCSE. gradientvelocity The gradient indicates the velocity of the object as shown on the next slide. Displacement and Velocity-Time graphs

You should be able to pull out 5 distinct regions. Describe each with numerical information. Calculating the velocity at a point or the average velocity……. Showing how you did it as well.

Velocity (m/s) Time (s) A B C D E FCyclist 1 Cyclist 2 Graph 2: Showing Velocity v time for two cyclists In this case there is even more information to gain from the graph. See how much you can work out…. Velocity-Time graphs

Velocity (m/s) Time (s) A B C D E F Cyclist 1 Cyclist 2 Graph 2: Showing Velocity v time for two downhill mountain bikers Cyclist 2 exhibits uniform acceleration The acceleration is rate of change of Velocity a = (v-u)/t a = (30 –0)/6 a = 5 m/s 2 You could do the same for each section of the graph for rider 1 giving answers of A  B = 10 m/s 2 B  C = 20 m/s 2 C  D = O m/s 2 ie Constant Velocity 40 m/s 1 D  E = - 20 m/s 2 Slowing down!

This is the same as the area under the red line just a different shape. So therefore the area under the second graph must also be the distance covered. Area under a Velocity-Time graph is the distance covered Gradient of a Velocity-Time graph is the acceleration. Velocity (m/s) Time (s) A Graph 2: Showing Velocity v time for two downhill mountain bikers What else does the graph show? If the graph was a straight line it would produce a nice neat rectangle underneath. You could understand that the area under the line is the distance covered since Distance = velocity * time

Worksheet – Velocity time Graphs

Not all graphs will be nice straight lines we may get curves at A Level so we need to understand that: velocity - dx/dt acceleration - dv/dt Where the dx/dt means the change in x divided by the change in time you are effectively talking about instantaneous rates of changes of displacements and velocities ie instantaneously changing velocities and accelerations may well be a curve. you are looking at the gradient of a line which may well be a curve. EXTRA! - Graphical Motion

) 2 1,t (x 1 2 ) x/m Time /s t tangent We are finding the gradient at time t. There is only one tangent that can be drawn. It touches the curve at t only. gradient = Dx/ Dt = (x 2 -x 1 )/(t 2 -t 1 ) This is negative - direction Note that you find the changes, Dx and Dt, by using the coordinates, not the length of the line!

You will now be familiar with the displacement time graph and the velocity time graph. Remember the following: Displacement time graph Velocity time graph AreaGradient “vt” DISTANCE TRAVELLED dx/dt VELOCITY dv/dt ACCELERATION

The Displacement Time Curve

Velocity Time Graphs

VelocityTimeGraphs

Example Sketch velocity vs time and displacement vs time for a ball thrown in the air and allowed to fall back to the ground - ignore air resistance. (0,0) Time /s x / m

Example Sketch velocity vs time and displacement vs time for a ball thrown in the air and allowed to fall back to the ground - ignore air resistance. You should note the symmetry.

Displacement Time Velocity Time So what happens when the ball bounces??

Displacement Time Velocity Time Acceleration Time

What do all these graphs tell us? upwards displacement is positive 1: The displacement is never zero as the centre of the ball doesn’t touch the ground and we have decided that an upwards displacement is positive Displacement Time Velocity Time Acceleration Time negativepositive 2: When the ball is in contact with the ground the ball’s velocity instantly changes from negative – downwards, to positive – upwards constant, negative acceleration due to gravity 3: In the air the ball experiences constant, negative acceleration due to gravity velocity changes from negative to positivevery quickly large, positive acceleration 4: During the bounces the velocity changes from negative to positive very quickly indicating a large, positive acceleration – much greater than the acceleration due to gravity!

 Factsheet 52