Speed Time Graph

Speed Time Graph and Acceleration

Introduction:


Before we get into understanding the relationship and graph between speed and time, its better to have an idea of these two concepts individually.

Speed and time are terms which are commonly used in our daily life. So, what is Speed? What are its units? Let us spend a few moments to get to know them. He started to move and gained speed. The cheetah saw the prey and started to move rapidly increasing its speed. Here the word speed refers to the rate at which distance is covered by a person, animal or object in a given time. Its just a number indicating the distance covered. It does not include direction per-se when we talk of speed. A parameter that has magnitude, but no direction is called a SCALAR quantity and the one that has speed and direction is a VECTOR. Here speed has magnitude alone with no direction, hence speed is a Scalar quantity. 
 
A fast-moving object like a race car covers a large amount of distance in a short period of time while a turtle covers a very short distance in a comparatively long period of time. Hence the former is supposed to be moving at high speed and the latter is supposed to be moving at slower speed. 
 
The dimension of speed is indicated by the dimension of distance divided by the dimension of time. In essence, you can show it as m/s or km/hr. As a matter of information when you are on sea or are flying, the unit of speed in knots. 1 knot is equal to 1.85 km/hr. The SI unit is m/s or km/hr and the SI unit does not include knots. Light has the fastest speed which is 3 x 108 m/s.
The Italian physicist is supposed to have first measured speed and arrived at the definition of distance covered in unit time.


 When you represent this in the form of an equation it is shown as,
V=d/t, where V is the speed, d is the distance covered and t is the time in which it is covered. The speed at any given instant is called an instantaneous speed. For example, when you are in a car, the speed shown by the speedometer is the speed at that particular instant. Average speed is the total distance covered by the total time taken. 
 
Now to understand the concept of time in brief. It is one of the most difficult concepts to understand. It is one of the most basic concepts, which is not made of up of anything else. For instance, a chemical has, molecule, atoms etc as its basic components. Time, however, has nothing simpler than itself hence it is the most basic concept by itself. You can say time as what the clock reads as we see. According to Sir Isaac Newton, in his classical physics, ABSOLUTE TIME existed independent of the perceiver. It is progressing at a continuous pace, cannot be perceived but can be measured and it can be expressed only in mathematical form. He further went on to state that what we perceive in day to day life is only relative time or apparent time and not absolute time. 
 
Then came Albert Einstein with the concept of relativity and relativistic time. His concept superseded Newtonian concept of time. In relativity, time is part of the universe and is not external or independent of it. Space-time is integral and not independent and that is why an event is always a point in space-time. Something happens at a given place at a given time. Einstein then established the concept of time-dilation proving that time is not the same for every observer and that it is relative. All these went completely counter to the Newtonian concept of time in classical physics. 
 
Now let us try to understand the relation between speed and time and see how it is graphically represented.

Speed-Time graphs:


In a speed-time graph, speed is always shown on the Y-axis or the vertical axis and time are shown on the horizontal or X-axis.
Initial speed is represented by the alphabet “u” and final speed is represented by the alphabet “v”. Time is represented as “t”.
If an object is starting from rest, then its initial speed is 0. Imagine a vehicle starting from rest then increasing speed to 15m/s in 10 seconds. It then travels at the same constant speed for another 10 seconds. From the 20th second, it increases speed to 25m/s for another 10 seconds. Suddenly the vehicle sees a rabbit darting across and begins to apply brakes and comes to rest in 20 seconds. So, its final speed is again 0.



The key thing here is, between the 10th and the 20th-second vehicle is moving at a constant speed so it shows up as a horizontal line. Do not confuse this with the Distance-Time graph and assume the vehicle not to be moving. That is wrong. Here is the speed is constant and so it shows up as a straight horizontal line. From 15 m/s to 25 m/s vehicle accelerates in 10 seconds. In this graph, you can calculate the gradients at different points. When you calculate the gradients in this graph you get the acceleration which is the rate of change of speed.

Whenever a body travels at a steady speed, there is no acceleration. In this case between the 10 and 20th second, the vehicle is traveling at a steady speed so there is no acceleration or the acceleration is 0m/s2. When you have to calculate acceleration it is always final speed – initial speed divided by the time. 
 
Hence in the first 10 seconds, the vehicle goes from 0 to 15 m/s. Here the final speed is 15 and the initial speed is 0 and all this happens in 10 seconds. To calculate the acceleration for this particular section you do 15 – 0 = 15/10 which is 1.5m/s2. If you take the last section where the vehicle had to apply brakes because of the rabbit coming in between, and it comes to a stop. So here the final velocity is 0 and the initial velocity 25m/s. 
 
So it is 0-25 = -25m/s which is the change in speed and this happens in a time of 20 seconds. So the acceleration is -25/20 which is -1.25 m/s2. Here you see the "negative" sign. This indicates the opposite of acceleration which is a decrease in speed also called deceleration. If you calculate the area under the graph you will get the distance traveled. The distance traveled is 675m. Convert the portion under the graph into squares, rectangles or triangles. Find the area of each and add them all up to give the total distance.

The units can be kms for distance and hours for time and in that case, the speed will be given as km/hr.

Acceleration and its unit:


What is the acceleration? The rate at which speed changes is defined as acceleration. In day to day parlance, acceleration refers only to increase in speed. When an ad for a vehicle says 0 to 100 in 5 seconds, this commonly refers to what is referred to as acceleration. 

In physics, acceleration is referred to an increase in speed and its opposite is called deceleration. Also, there is another aspect of acceleration caused to change in direction. Even if there is no change in speed but if the direction changes there is acceleration. The reason being, velocity is a vector quantity. Any vector quantity has magnitude and direction, so in the case of acceleration, even if the magnitude does not change but if the direction changes there is acceleration. For example: in a circular motion, there is what is called centripetal acceleration. Like speed acceleration also has instantaneous acceleration and average acceleration. Acceleration measured over a very very short interval is instantaneous acceleration. 
 
Acceleration is given by change in speed(m/s) divided by time(s) so acceleration is given in m/s2.