Derive the equation of motion S = u + a/2 * (2n - 1) by graphical method.
Answers
Answer:
To Derive 2nd equation of motion [Graphically.]
★ sut + 1/2 at²
Consider the velocity time graph of a body
shown in attachment. The body has an initial
Velocity u at point A and then velocity changes
from A to B at a uniform rate in time t. There's
uniform acceleration a from A to B,and after
time t the final Velocity is v which is equal to BC.
The time t is represented by OC. Through
construction we drew perpendicular CB from
point C,and AD parallel to OC. BE is
perpendicular to the point B to OE.
Here,
• Initial Velocity (u) = OA
• Final Velocity (v) = BC
• Time (t) = OC
Distance Covered = Area of the figure OABC
Area of OABC = Area of OADC + Area of ABD
→ Distance (s) = Area of OADC + Area of ABD
→ S = (OAX OC) + (1/2 x AD x BD)
→s= (u × t) + (1/2 x tx at)
→s=ut + 1/2 at²
.. The 2nd equation of motion is derived here graphically.
