Question

A = sin ti + cos tj + tk, evaluate
d2A/dt2

Answer 1

Answer on Question #62252 – Math – Analytic Geometry

Question

$$A = \operatorname{sin t} i + \operatorname{cost} j + t k,$$ $$\frac{d^{2} A}{dt^{2}} = ?$$

Solution

Let's derive vector $A$ twice:

$$\frac{d A}{d t} = (\sin t)' i + (\cos t)' j + (t)' k = \cos t i - \sin t j + k,$$ $$\frac{d^{2} A}{d t^{2}} = (\cos t)' i - (\sin t)' j + (1)' k = - \sin t i - \cos t j + 0 k = \sin t - \cos t j.$$

Answer: $\frac{d^{2} A}{dt^{2}} = \sin t - \cos t j$.

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