A particle moves in a circle of radius 30 cm. Its linear speed is given by v = 2t, where t in second and v in m/s. Find out its radial and tangential acceleration at t = 3 s.A 220 m/s2, 50 m/s2 B 100 m/s2, 5 m/s2 C 120 m/s2, 2 m/s2 D 110 m/s2, 10 m/s2
Question
A particle moves in a circle of radius 30 cm. Its linear speed is given by v = 2t, where t in second and v in m/s. Find out its radial and tangential acceleration at t = 3 s.A 220 m/s2, 50 m/s2 B 100 m/s2, 5 m/s2 C 120 m/s2, 2 m/s2 D 110 m/s2, 10 m/s2
Solution
To solve this problem, we need to understand that radial and tangential acceleration are given by the formulas:
Radial acceleration (ar) = v^2 / r Tangential acceleration (at) = dv/dt
Given that v = 2t and r = 30 cm = 0.3 m, we can substitute these values into the formulas.
First, let's find the tangential acceleration at t = 3 s. Since v = 2t, dv/dt = 2. Therefore, at = 2 m/s^2.
Next, let's find the radial acceleration at t = 3 s. We first need to find v at t = 3 s. Substituting t = 3 s into v = 2t gives v = 2*3 = 6 m/s. Now we can substitute v = 6 m/s and r = 0.3 m into the formula for radial acceleration to get ar = (6 m/s)^2 / 0.3 m = 120 m/s^2.
So, the radial and tangential accelerations at t = 3 s are 120 m/s^2 and 2 m/s^2, respectively. Therefore, the correct answer is C. 120 m/s^2, 2 m/s^2.
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