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Q.

Is it true that the second equation of motion is $s = ut + \frac{1}{2} a t^{2}$ ?

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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 Image

Question Image

We can conclude from the graph above that

Distance travelled (s) = Figure area OABC

\Rightarrow = Area of rectangle OADC + Triangle Area ABD

s = (\frac{1}{2} \times AD \times BD) + (OA \times OC)

The above equation becomes, as

OA = u

and

OC = t .

s = (\frac{1}{2} \times AD \times BD) + (u \times t)

The equation becomes, as

BD = at

(from the graphical derivation of the first equation of motion).

s = \frac{1}{2} \times t \times at + ut

Further simplifying the equation, it becomes

s = ut + \frac{1}{2} a t^{2}

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