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}}} $

Show Answer

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} $



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