Question

Derive the equation of motion

S=ut+(1/2)at2 graphically

Answer 1

Answer:

Explanation:

Consider the linear motion of a body with an initial velocity u. Let the body accelerate uniformly and acquire a final velocity v after time t. The velocity–time graph is a straight line AB as shown in attachment.

 

At t = 0, initial velocity = u = OA  

At t = t, final velocity = v = OC

The distance S travelled in time t = area of the trapezium OABD

s = (1/2) x (OA + DB) × OD

s = (1/2) x (u + v) × t  

Since v = u + at,

s = (1/2) x (u + u + at) × t

s = ut + (1/2) at2  

Answer 2

Derive the second equation of motion s = ut + (1/2)at^2 using the velocity-time graph. Derive the second equation of motion s = ut + (1/2)at2 using the velocity-time graph. ... Let the body accelerate uniformly and acquire a final velocity v after time t. The velocity–time graph is a straight line AB as shown below.