Traveling in vehicles has become an important part in our daily lives
Say, we have a truck which moves in a straight line from A to B, over a distance of 100 km in 4 hrs
We know that
Velocity = TimeDisplacement
Since the truck is travelling in a straight line, displacement = 100km
Hence, the velocity = 4hrs100km=25km/hr
But, we must remember that this is only the average velocity
It is possible that the truck is not moving the entire time with a velocity of 25km/hr
It can encounter a traffic signal, say at point C, where it has to slow down to rest
Or it can increase it's speed up on a highway
So, the truck may not have constant velocity throughout it's journey. It may have to speed up or come to rest depending on different situations
Such a motion, where the velocity of a moving vehicle is changing with time, is called as "accelerated motion"
We define acceleration to be the rate of change of velocity
Acceleration of an object is defined to be the rate of change of velocity of that object
Mathematically, Acceleration=Change in TimeChange in Velocity
If the velocity increases with time, then the object is said to have "Positive Acceleration", while if the velocity decreases, it is called "Deceleration"
Let us try to plot the velocity and time on a graph
On a graph, we plot Velocity on the Y Axis and Time on the X axis to get the Velocity-Time Graph
Case 1: Let us assume that the vehicle is moving with a constant velocity of 50km/hr over a time interval of 0−5hrs
The Velocity-Time Graph would look something like this
The area under the Velocity-Time Graph gives the Displacement in the time interval
We can prove it analytically as: Displacement=Velocity×Time⟹ Displacement after 5 hrs = 50×5=250km
From the graph area under the curve = area of rectangle AOCD = 50×5=250km
The slope of the Velocity-Time Graph gives the value of Acceleration
Since the vehicle is moving with a constant velocity, the acceleration = 0
We can also say from the graph since the velocity plot is parallel to the time
Case 2: Let us assume the vehicle is moving with a velocity starting from rest, that is constantly increasing over a time interval of 0−5hrs
The Velocity Graph would look something like this
On similar lines, the displacement can be obtained from the area under the curve
Displacement =21(50)(5)=125km
Here, the acceleration is not 0, since the velocity is constantly changing with time
Acceleration =5−050−0=10km/hr2
The velocity increases by 10km/hr every 1hr
Case 3: Let us assume that the vehicle is moving with a velocity that is constantly decreasing over a time interval of 0−5hrs and finally coming to rest
The Velocity-Time graph would look something like this
Displacement = Area under the curve = 21(50)(5)=125km
The Acceleration is negative in this case, since the velocity is constantly decreasing over time
Deceleration =5−00−50=−10km/hr2 (Since the initial velocity is taken to be 50km/hr)
The velocity is decreasing by 10km/hr every 1hr
Revision
Average Velocity =
(Total Displacement)/(Total time)
Acceleration =
(Change in velocity)/(Change in time interval)
Velocity-time graph is a graphical representation of the motion of an object with the Velocity on the Y-Axis and Time on the X-Axis
For constant velocity, the v−t curve is a horizontal straight line. For uniformly accelerated motion, its a straight line with positive slope
For uniformly decelerated motion, its a straight line with negative slope