IGCSE Coordinated Science: Motion

IGCSE Coordinated Science: Motion Motion 1. Define speed and calculate speed from: ❖ The speed of an object is the distance it travels per unit time. We quantify this as the ratio of the distance it travels to the time taken to travel that distance. ❖ The formula for speed is above and the units are ms-1 or m/s. Ex. Michael runs a marathon. He runs 40km in 2 hours. What is his average speed? Well, the distance Michael travels is 40km. He does this in 2 hours. Therefore, using the formula Speed= Distance/Time, we get: Speed = 40 km / 2 hours Speed = 20 km / hour 2. Distinguish between speed and velocity. We don’t really touch upon this during GCSE, but it doesn’t hurt to get some additional knowledge. Basically, speed and velocity are both different type of quantities. The two types of quantities are: ❖ Vector ❖ Scalar Vector quantities have both a magnitude and direction. Scalar quantities only have a magnitude but no direction. That is the fundamental difference between velocity and speed. Velocity is a vector whilst speed is a scalar. Velocity not only measures how fast something travels, but also the direction it is traveling in, something the speed neglects. 3. Plot and interpret a speed/time graph and a distance/time graph. It is often useful to be able to map the relations between speed, distance and time graphically. The graph below will show a speed/time graph where we measure how speed is changing according to time. ❖ Speed/Time Graph Green line: Constant acceleration. Orange Line: If you look at the y-axis, speed doesn’t change, so we can say the object is travelling with a constant speed. Blue line: Object is now decelerating, in which change in velocity is now a negative value. ❖ Distance/Time Graph Notes: ❖ Green line: Speed of the object is constant, and can be found by dividing Distance by Time. We can tell speed is positive as both time and distance travelled are also both positive. ❖ Orange line: Distance is not changing so object remains stationary with no movement. ❖ Blue line: Steady speed returning to the start. The red line is steeper than the green line, so therefore it is travelling at a faster speed. Steepness is basically a measure of the gradient of the Distance/Time graph, which is also the speed of an object. The steeper the graph, the higher the gradient, and therefore the faster the speed. 4. Recognise linear motion for which the acceleration is constant and calculate the acceleration. The situation above mainly shows cases where the acceleration is constant. We can test that this is true by finding the gradient of the line. We can find the distance simply by dividing Change in speed by Time, which if you look carefully enough, is the formula for acceleration. Here, we say that the speed is proportional to time and that acceleration (the gradient) is constant throughout the journey 5. Recognise motion for which the acceleration is not constant. In Q5, we learned how to calculate acceleration when it is a constant value on a Speed/time graph. However, in the real world, this is rarely the case. Rarely can you accelerate with “constant” velocity and more likely than not, the acceleration of an object is going to change around a bit. Here is an example of a graph where the gradient is not constant. Notice when the speed/time graph is not a straight line (proportional relation), then the acceleration is not constant. You just have to be able to appreciate this fact, and will not be asked to make any calculations. However, in IB/A-level math, you will have to make these quite pointless calculations . 6. Calculate the area under a speed/time graph to work out the distance travelled for motion with constant acceleration Using the given information above, you can easily calculate the distance travelled. Remember the formula Speed= Distance/Time . If we re-arrange the formula, we get Distance = Speed x Time. . Notice here, Speed x Time is equivalent to the area of the graph. Let’s calculate the distance travelled. It’s simply the area under the shaded orange triangle. Now, we simply have to apply some simple mathematical skills. What’s the area of a triangle? Area of Triangle = (Base x Height)/2 Base = Time = 8 seconds Height = Speed = 10meter/second (Base x Height)/2 = (8 secondsx10 meters/second)/2 =40 meters. 7. Demonstrate a qualitative understanding that acceleration is related to changing speed. Acceleration is the measure of the change of speed of an object per unit time, more specifically, the velocity of the object, and we’ve definitely talked about their differences.