Distance, Time & Speed

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One of the important topics in physics is to understand the laws which govern the motion of bodies through space. The actual laws are complex and need higher math topics like calculus to understand them. But simpler types of motion can be understood with the math that we learn in primary school.

We must first understand some vocabulary associated with motion of bodies through space.

Distance

This is the distance by a body in motion.

Time
 * 1) The distance may be given directly as say 3 kms.
 * 2) Or it may have to be deduced from given data. For example, it may be given that a car starts from a milestone which says it is 40 kms from Pune. It may have to travel on that road to a point which is 15 kms from Pune. Hence, we can deduce that the car has to travel a distance of 25 kms (40 – 15).

Another concept is the time taken to travel a particular distance.

Speed
 * 1) In the above example, you may be provided data that the distance of 25 kms was covered in 45 minutes.
 * 2) Or the time taken may be provided in an indirect way as follows. The car starts at t he 40 kms mark at 3.30 p.m and reaches the 15 km mark at 4.15 p.m. We can then figure out from the given data that it has taken 45 minutes.

Speed is a concept which is related to both the distance and the time during which it is covered. Intuitively we know the following relations between distance, time and speed.

Power of Math
 * 1) If the speed is more then the same distance is covered in a shorter interval of time. By the same logic, if the speed is less, then the same distance will be covered in a longer period of time.
 * 2) If the speed is more then in the same period of time, a longer distance would be covered. By the same logic, if the speed is less, then in the same period of time, a shorter distance would be covered.

The above explanations in text were long and some people may find it difficult to read them and understand. But the same idea can be captured very easily with math. That is the power of math. We can write the relation between distance covered (d), time taken (t) and speed of travel (s) as given below.

s =

We can easily see that the explanations under &ldquo;speed&rdquo; are apparent if we consider the above equation. S would increase if either &ldquo;d&rdquo; increases or &ldquo;t&rdquo; decreases. On the other hand, s would decrease if &ldquo;d&rdquo; decreases or &ldquo;t&rdquo; increases.

s = also tells us that t = , ie the time taken for a journey can be got by dividing the distance covered by the time taken.

s = also tells us that d=st, i.e the distance travelled can be got by multiplying the speed and the time taken.

Average Speed

There is another concept we need to be familiar with. When a car travels, it cannot travel at the same speed from start to finish. Its speed starts from 0, increases gradually and at the end, the speed would decrease gradually and become 0. On the way, speeds will keep on changing depending on the traffic and condition of the road. So in the above equation, &lsquo;s&rdquo; denotes the &ldquo;average&rdquo; speed of the car. It gives us a rough idea of the speed at which the car was travelling.

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