Derive the second equation of motion by graphical method
Asked by admin @ in Biology viewed by 323 People
Derive the second equation of motion by graphical method
Asked by admin @ in Biology viewed by 323 People
Derive the second equation of motion by graphical method
Answered by admin @
★ s = ut + ½ 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 = (OA × OC) + (½ × AD × BD)
→ s = (u × t) + (½ × t × at)
→ s = ut + ½ at²
The 2nd equation of motion is derived here graphically.
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