Hi and welcome back to freesciencelessons.co.uk. 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 higher tier student, then you should be able to calculate the distance travelled 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 in meters per second, divided by the time in seconds. I've also given you 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 travelling at a velocity of 15 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 divide the change in velocity by the time taken. The final velocity was 35 meters per second north, and the start velocity was 15 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 20 second period. Try this question. A cyclist is traveling at a velocity of 6 meters per second east.
Her velocity reduces to 0 in 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 0 meters per second east, and the start velocity was 6 meters per second east. So the change in velocity is 0 minus 6 meters per second. This gives us a change in velocity of minus 6 meters per second.
This took place over 12 seconds. Putting these into the equation gives us an acceleration of minus 0.5 meters per second squared. In this case the object is 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. Now a 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 object's 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 and divide by the time. 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 0.15 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 15 meters per second. the time was 300 seconds. Putting these into the calculation gives us an acceleration of minus 0.05 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 higher tier 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 travelled 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 2250. Adding these together, gives us a total distance or displacement of 4500 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 add up to approximately five 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 5000 metres.
Remember you'll find plenty of questions on acceleration and velocity time graphs in my revision workbook, and you can get that by clicking on the link above.