[Music] I'm welcome back to free size lessons code okay by the end of this video you should be able to describe what's meant by acceleration you should then be able to calculate the acceleration of an object and if you're a high tier student then you should be able to calculate the distance traveled by an object from a velocity time graph in a previous video we looked at the idea of velocity the velocity of an object is its speed in a given direction velocity is a vector quantity as it has both magnitude and direction the acceleration of an object tells us the change in its velocity over a given time and we calculate acceleration using this equation acceleration in meters per second squared equals the change in velocity and meters per second divided by the time in seconds I've also given me the triangle for this equation now you're not given this equation in the exam so you need to learn it here's a typical question a car is traveling at a velocity of 50 meters per second north it accelerates to a velocity of 35 meters per second north in 20 seconds calculate the acceleration of the car so pause the video now and try this yourself okay so to calculate acceleration we divided the change in velocity by the time taken the final velocity was 35 meters per second north and the start velocity was 50 meters per second north so the change in velocity is 35 minus 15 giving us a value of 20 meters per second the time taken was 20 seconds putting these into the equation gives us an acceleration of one meter per second squared so what that means is that the car increased its velocity by one meter per second every second over a twenty second period try this question a cyclist is traveling at the velocity of six meters per second east a velocity reduces to zero and 12 seconds calculate the acceleration of the cyclist again pause the video and try this yourself okay the acceleration equals the change in velocity divided by the time taken the final velocity was zero meters per second East and the start velocity was six meters per second east so the change in velocity is zero minus six meters per second this gives us a change in velocity of minus six meters per second this took place over 12 seconds putting these into the equation it gives us an acceleration of minus not 25 meters per second squared in this case the object slowing down and scientists call this deceleration now we can also calculate the acceleration of an object using a velocity time graph so we're going to look at those now I'm showing you a velocity time graph here and you could be asked to plot one of these in your exam our key fact is that the gradient of a velocity time graph tells us the acceleration of the object in the case of a horizontal line like this the objects traveling at a constant velocity an upward sloping line shows that the object's accelerating whereas a downward sloping line shows that the object is decelerating so we're going to calculate the acceleration in the first part of the graph to do that we subtract the initial velocity from the final velocity under vide in this case the final velocity is 15 meters per second and the initial velocity was zero and the time is 100 seconds putting these into the calculation gives us an acceleration of naught point one five meters per second squared looking at the last part of the graph we can see that the final velocity is zero and the initial velocity was fifteen meters per second the time was 300 seconds pudding listen to the calculation gives us an acceleration of minus naught point naught five meters per second squared in this case the negative number tells us that the object was decelerating okay now foundation tier students can stop watching however high attea students need to continue so as we've seen the gradient of a velocity time graph tells us the acceleration however the total area under the graph tells us the distance traveled in a specific direction in other words the displacement now when we see constant acceleration or deceleration then we simply divide the graph into shapes and calculate the total area so we've got a triangle with an area of 750 a rectangle with an area of 1500 and a triangle with an area of 2,250 adding these together gives us a total distance or displacement of 4,500 meters now you might see a velocity time graph like this in this case the acceleration and deceleration are not constant to calculate the total area under the graph we need to count squares in this case there are 15 complete or almost complete squares we then have to estimate the total of the parts of squares these are up to approximately 5 squares so the total number of squares under the graph is 20 each square has an area of 250 multiplying 20 by 250 gives us a total distance or displacement of 5,000 meters remember you'll find plenty of questions on acceleration on velocity time graphs in my vision workbook and you can get that by clicking on the link above [Music] you