Show by using the graphical method that: `s=ut+1/2at^2` where the symbols have their usual meanings.
Suppose the body travels a distance (s) in time (t).
In the figure, the distance travelled by the body is given by the area of the space between the velocity-time graph AB and the time axis OC, which is equal to the area of the figure OABC.
Thus: Distance travelled = Area of the trapezium OABC
But, Area of the figure OABC = Area of rectangle OADC + Area of triangle ABD
= Area of rectangle OADC + area of triangle ABD
Now, find out the area of rectangle OADC and area of triangle ABD.
(i) Area of rectangle OADC
= (OA) (OC)
= (u) (t)
(ii) Area of triangle ABD,
Distance travelled (s) is,
So, s = Area of rectangle OADC + Area of triangle ABD
`s = ut + 1/2at^2`
This is the second equation of motion.
(s) - Displacement
(u) - Initial velocity
(a) - Acceleration
(t) - Time
Video Tutorials For All Subjects
- Graphical Representation of Motion: Velocity - Time Graphs