question_answer

A particle moves in circle of radius 20cm. Its linear speed is given by \[\upsilon =2t\]where t is in second and in metre/second. Find the radial and tangential acceleration at \[t=3s\].

Answer:

                Linear speed at \[t=3s\]is \[\upsilon =2t=2\times 3=6m/s\]. Radial acc. At this instant \[{{a}_{r}}=\frac{{{\upsilon }^{2}}}{r}=\frac{6\times 6}{0.20}=180m/{{s}^{2}}\] Tangential acc. is \[{{a}_{t}}=\frac{d\upsilon }{dt}=\frac{d}{dt}\left( 2t \right)=2m/{{s}^{2}}\]