Answer:
Let at
an instant t,
\[\upsilon\]
be the velocity of the moving particle and s be the
distance travelled by the particle. As per question.
\[\text{s }=\text{ }\upsilon \text{t}/\text{2}\] ...(i)
Differentiating it w.r.t. time t, we have
\[\frac{ds}{dt}=\frac{1}{2}\frac{d\upsilon
}{dt}\times t+\frac{\upsilon }{2}\]
Or \[\upsilon =\frac{1}{2}a\times
+\frac{\upsilon }{2}\]
or at = \[\upsilon \]
Differentiating it again w.r.t. time t, we have
\[\frac{da}{dt}\times \text{t }+\text{ a }=\frac{d\upsilon
}{dt}=\text{ a}\]or\[\frac{da}{dt}\times \text{t =}\,\text{0}\]or\[\frac{da}{dt}\text{=}\,\text{0}\]
Therefore ; a = a constant.
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