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Q.

Is it true that the second equation of motion is s = ut + 12at2?


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a

True

b

False 

answer is A.

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Detailed Solution

The above statement is true.
The second equation of motion is obtained by taking the area under the velocity time graph. The second equation of motion of a body under the velocity time graph connects the displacement (s), initial velocity (u), acceleration of the body (a), and the time period of the body (t). First the area under the velocity time graph is mathematically calculated and later the quantities are substituted.
Question ImageWe can conclude from the graph above that
Distance travelled (s) = Figure area OABC 
⇒                                        =Area of rectangle OADC + Triangle Area ABD
 s=12×AD×BD+(OA×OC)
The above equation becomes, as OA=u and OC=t.
 s=12×AD×BD+(u×t)
The equation becomes, as BD =at (from the graphical derivation of the first equation of motion).
 s=12×t×at+ut
Further simplifying the equation, it becomes
 s=ut+12at2
 
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