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Which of these gives the distance travelled?
How fast is Phillip riding his scooter? What's his speed? Well, look at the speedometer. It reads 20 kilometers per hour, but what does that mean to travel 20 kilometers per hour? Phillip hasn't been going nearly as far as 20 kilometers, and he won't be riding for an hour either.
Still, his speed is 20 kilometers per hour. What it means is this: Phillip is traveling at a speed which if he kept it steadily for an hour, would take him a distance of 20 kilometers. If he keeps going for two hours, then he will travel a distance of 40 kilometers. Speed multiplied by time equals distance. Phillip keeps traveling at the speed of 20, no, 25 kilometers per hour.
30, easy Philip. Which speed should we use in the formula when the speed keeps changing all the time? The speedometer shows how fast the scooter is going right now. It shows the instantaneous speed, but that doesn't really help Philip. He wants to know the speed for his entire journey.
Maybe he should make a note of the instantaneous speed at, say, every five seconds, and then calculate the average. Nah, that sounds dangerous. There is a simpler way to calculate the speed of an entire journey, even if the instantaneous speed has changed. And it's written right there on the speedometer - kilometers per hour. Kilometers divided by hours.
Distance divided by time equals speed. Philip has traveled a total of four kilometers, and it took him a quarter of an hour. Four kilometers divided by one-quarter of an hour. Four divided by one-quarter is 16. Philip made his trip to the pharmacy with an average speed of 16 kilometers per hour.
Let's make a diagram to show how speed works. On the X-axis, there's time in hours. On the Y-axis, we have distance in kilometers. Here's Philip's trip to the store. Steady at first, then speeding up.
Then he stops at a red light and the distance doesn't increase at all for a while, but time keeps going. The light is green and he's off moving again, increasing the speed, and he reaches the store. The distance is now four kilometers. The time is one-quarter of an hour, but where is the speed in the diagram? Can you tell from the diagram when Philip is traveling the fastest?
The speed is the slope of the line. When the line is steep, Philip covers a lot of distance in a short time- a high speed. When the line is flat, the distance doesn't change at all. Philip is standing still. Do you remember how we calculated the average speed?
Kilometer per hour- distance divided by time. If Philip would have traveled at the average speed for the entire journey, the trip would have taken exactly the same amount of time. Can you figure out how the journey would be plotted in the diagram if he rode at the average speed throughout? This is what it would look like. The speed is the slope of the line and if the speed is constant, then the line has the same slope over its entire length.
When we talk about scooters and cars, we often measure the speed in kilometers, or miles per hour. But in physics, we use meters per second. One meter per second is 3.6 kilometers per hour, because there are 3,600 seconds in an hour and 1,000 meters in a kilometer. As long as you make sure to use the same units throughout your calculations, this little triangle here can help you with most speed-related problems. Speed equals distance divided by time.
Distances equals speed times time. Time equals distance divided by speed.