Kinematics Question 656
Question: A particle moves in a circle of radius 30 cm. it’s linear speed is given by: $ V=2t $ , where t in second and v in m/s. Find out it’s radial and tangential acceleration at t = 3 sec respectively.
Options:
A) $ \text{220 m/se}{{\text{c}}^{\text{2}}}\text{, 50 m/se}{{\text{c}}^{\text{2}}} $
B) $ \text{110 m/se}{{\text{c}}^{\text{2}}}\text{, 5 m/se}{{\text{c}}^{\text{2}}} $
C) $ \text{120 m/se}{{\text{c}}^{\text{2}}}\text{, 2 m/se}{{\text{c}}^{\text{2}}} $
D) $ \text{110 m/se}{{\text{c}}^{\text{2}}}\text{, 10 m/se}{{\text{c}}^{\text{2}}} $
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Answer:
Correct Answer: C
Solution:
[c] Given: r = 30 cm = 0.3 m and V = 2t Radial acceleration at t = 3 sec
$ {{\text{a}} _{\text{r}}}\text{=}\frac{{{\text{v}}^{\text{2}}}}{\text{r}}\text{=}\frac{\text{4}{{\text{t}}^{\text{2}}}}{\text{0}\text{.3}}=\frac{\text{4 }\times{{( \text{3} )}^{\text{2}}}}{\text{0}\text{.3}}\text{=120 m/}{{\text{s}}^{\text{2}}} $
and trigeminal acceleration
$ a{ _{t}}=\frac{dv}{dt}=2m\text{/}s^{2} $
