Question

Show that 

i) v = u + at, 

ii) s = ut + 1/2at² in graphical method.

Answer 1

1) Graph is plotted with time on x – axis and velocity on y – axis. 

2) According to the above graph, 

Velocity of the object at “t” value ”0″ = u 

Velocity of the object at “t” value “t” = v 

3) Difference between the time intervals = v – u

4) From the graph, x₁ = 0, x₂ = t, y₁ = u, y₂ = v

Slope = \(\frac{y_2\,-\,y_1}{x_2\,-\,x_1}=\frac{v\,-\,u}{t\,-\,0}=\frac{v\,-\,u}{t}\)

5) We know that slope refers acceleration to the velocity – time graph. 

Hence acceleration (a) = \(\frac{v\,-\,u}{t}\)  ⇒ v – u = at ⇒ v = u + at ………… (1)

6) The area between the two straight lines drawn at u, v gives displacement of the object. The area of graph is in the shape of trapezium. It has a rectangle and a triangle. 

7) Area of the graph = area of rectangle (ABCD) + area of triangle (DCE)

8) We know that area of the graph of velocity – time gives displacement(s).