The position vector of a body, with respect to the origin, is given by \(r = 4ti + (12 - 3t)j\) at any time t seconds.
(a) Find the velocity of the body ;
(b) Calculate the magnitude of the displacement between t = 0 and t = 5.
(a) Find the velocity of the body ;
(b) Calculate the magnitude of the displacement between t = 0 and t = 5.
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Correct Answer: Option n
Explanation:
\(r = 4t i + (12 - 3t)j\)
(a) \(v = \frac{\mathrm d r}{\mathrm d t} = 4i - 3j\)
(b) When t = 0, r = 0i + 12j = 12j.
When t = 5, r = 20i - 3j.
Displacement = \(r_{t = 5} - r_{t = 0}\)
= \(20i - 3j - 12j\)
= \(20i - 15j\)
\(|Disp| = \sqrt{20^{2} + 15^{2}} = \sqrt{400 + 225}\)
= \(\sqrt{625} = 25m\)
\(r = 4t i + (12 - 3t)j\)
(a) \(v = \frac{\mathrm d r}{\mathrm d t} = 4i - 3j\)
(b) When t = 0, r = 0i + 12j = 12j.
When t = 5, r = 20i - 3j.
Displacement = \(r_{t = 5} - r_{t = 0}\)
= \(20i - 3j - 12j\)
= \(20i - 15j\)
\(|Disp| = \sqrt{20^{2} + 15^{2}} = \sqrt{400 + 225}\)
= \(\sqrt{625} = 25m\)