What other quantities must be accompanied by a direction as well as its size?
What physical quantities do we need to be able to work out the acceleration of something? Mark Cavendish – video clip of tour de France, final stage (21, coming into Paris at the Arc de Triomphe). During the last 200 m Cav is known as a legend for accelerating up to 48 mph to snatch a win (world record for someone from the UK, winning 6 stages at only 24 years-old)
Michael Johnston left speechless! http://news.bbc.co.uk/sport1/hi/athletics/8204766.stm First 30 m, t = 3.78 s, u = 0 m/s, v = 11.11 m/s, a = 2.94 m/s^2 Last 20 m, t = 9.58 - 7.92 = 1.66 s , u = 12.20 m/s, v = 12.05 m/s, a = -0.09 m/s^2
Shallow slope up Steep slope up Slope down Negative Positive low Positive high Continually changing Steep to shallow Shallow to steep
Wind-up racer’s motion
Red Bull Stratos – Felix Baungartner and Joe Kittinger As this piece of historic motion is yet to be done we unfortunately don’t have any speeds to work with but we were luck enough to catch up with Felix on a stretch of road through the country side where he allowed us to film. So here we go, pens at the ready, take down the distance at 5 second intervals and then we’ll replay the high-octane action for speed.
Video clip of v-t, results table time 0 – 30, take results every second (vertically down) Time axis – every box 2 seconds Velocity axis – every box 5 m/s
Talk through the ‘journey’ Label acceleration, deceleration, speeding up, slowing down, steady speed, zero speed and low & high speed Calculate acceleration during 1 st five seconds – 12 m/s^2 From 5 s to 8 s (6-60)/3 = -18 m/s^2
Which is more impressive, Neo dealing with being shot at or Hancock saving someone’s life? How could we judge who is the most awesome? Vid clips, Neo with the bullet-stopping and Hancock with the train-stopping What did Neo do at the start of the clip and what physical factor was it that he so impressively controlled? Extremely fast speed (or velocity). Hancock did something similar but it was a different physical factor that made his ability so impressive, what was it? Both superheroes are controlling the ‘momentum’ of the objects, and in these examples each object has a great deal of momentum! In Science momentum is ‘ mass in motion ’ Momentum of a football team, they’re hard to stop – they’ve built up a lot of pace
The displacement of an object after a journey can be zero-
The total distance travelled was 50 metres
25m A B Journey A – B and then B - A A B Total displacement from A to B and B back to A… zero 10m
7.
Speed The rate at which an object changes the distance it has travelled is called its speed . For a complete journey the speed of an object can be calculated by dividing the total distance covered by the time taken to complete the journey- Average Speed = Total Distance / Time Taken metres/second = metre / second Ferrari 360 Spider speed distance time
The average acceleration of an object is given by the change in velocity per unit time-
Acceleration = Change in Velocity / Time Taken Acceleration = ( Final Velocity – Initial Velocity ) / Time Taken a = (v – u) / t m/s 2 = m/s / s a t Δ v
A value for the gradient of a graph can be calculated by dividing the change in the ‘y value’ by the change in the ‘x value’
0 15 75 y x 1.2 4.8 y x 0 Gradient = 75 / 15 = 5 Gradient = -4.8 / 1.2 = -4 Negative gradient, slope down
32.
The change in y is the distance the object has travelled The change in x is the time the object was travelling Speed equals distance divided by time, therefore the gradient of the graph is the same as the speed of the object
33.
What is the gradient, and hence the speed of the car? Change in y = Distance travelled = 800 – 200 = 600 m Change in x = Time taken = 36 - 16 = 20 s Gradient = Speed = Distance / Time = 600 / 20 = 30 m/s
We’ve seen how Distance-Time graphs can be a clear illustration of an object’s motion. Another usefully way to present this motion is in the form of a Velocity- Time graph.
Some of the common shapes that describe the motion of an object are-
Graphs of motion speed speed speed Increasing speed Decreasing speed Acceleration Constant speed Slower Acceleration Stopped Deceleration v v v v v v t t t t Slower constant speed
Consider this example- A car travels at 4 m/s for 10 s
Velocity / Time graph for the motion
Time (s) Velocity (m/s) 4 10 Wee Bit Extra
42.
Time (s) Velocity (m/s) 4 10 Velocity = Displacement / Time Area under the graph!! From the graph- Velocity = 4 m/s Time = 10 s Re-arrange the equation- d = v x t = 4 x 10 = 40 m v d t