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Laws of Motion — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysicsLaws of Motion3 Marks
Question
A particle moves in a circle of radius $20cm$. Its linear speed at any time is given by $v = 2t$ where v is in m/s and t is in seconds. Find the radial and tangential accelerations at $t = 3$ seconds and hence calculate the total acceleration at this time.
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Answer

The linear speed at 3 seconds is $v = 2 \times 3 = 6m/s$ The radial acceleration at 3 seconds $=\frac{\text{v}^2}{\text{r}}=\frac{6\times6}{0.2=180}=180\text{m/s}^2$ The tangential acceleration is given by $\frac{\text{dv}}{\text{dt}}=2,$ since $\text{v}=2\text{t}$
$\therefore$ tangential acceleration is $2/s^2$. Total acceleraton $\sqrt{\text{a}^2_\text{r}+\text{a}^2_\text{t}}=\sqrt{180^2+2^2}$
$=\sqrt{32400+4}=\sqrt{32404}\text{ms}^{-2}.$

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