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A particle is moving along \( \mathrm{x} \)-axis such that its position ' \( \mathrm{x} \) ' varies with time ( \( \mathrm{t}) \). Find the velocity (v) and acceleration (a) of particle if its position w.r.t time is given by :
\( \mathrm{P} \)
(i) \( \mathrm{x}=\mathrm{t}^{2} \)
(ii) \( \mathrm{x}=\frac{1}{\mathrm{t}} \)
(iii) \( \mathrm{x}=\frac{1}{\sqrt{\mathrm{t}}} \)
(iv) \( \mathrm{x}=\mathrm{t}^{3 / 2} \)
W
(v) \( \quad \mathrm{x}=\mathrm{t}^{5 / 2} \)
(vi) \( \mathrm{x}=\sqrt{2} \mathrm{t}^{2} \)
(vii) \( x=5000 \)
(viii) \( \mathrm{x}=\mathrm{t}^{2}+\mathrm{t}+5 \)
(ix) \( x=4 t^{3}+3 \)
(x) \( \quad \mathrm{x}=3 \mathrm{t}+\frac{2}{\mathrm{t}} \)
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