Question

Prove
s=ut + 1/2 (acceleration × time )square
Don't post irrelevant answers

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Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Step-by-step explanation:

How does s=ut+1/2 at^2?

There are two ways to prove this, either we use calculus or we do not.

Method 1

Consider a velocity-time graph where the object is moving at constant acceleration

(where u denotes initial velocity and v denotes final velocity)

The area of a velocity-time graph gives the displacement, therefore:

ss=Area of AOCD+Area of ADB=ut+12×t×(v−u)=ut+12×t×at∵v=u+at=ut+12at2

Method 2 (uses calculus)

Displacement is the integral of velocity with respect to time:

s=∫vdt

Substitute v=u+at into the integral:

ss=∫(u+at)dt=∫udt+∫atdt=ut+a∫tdt=ut+12at2+C

When t=0 , s=0∴C=0 , so our equation reduces to

s=ut+12at2

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