Answered: "What is the instantaneous velocity of an object..."

oerddrwsmqc

Answered question

2022-03-14

What is the instantaneous velocity of an object moving in accordance to

f (t) = (t^{2} \sin (t - π), t \cos t)

t = \frac{π}{3}

Jamiya Bradford

Beginner2022-03-15Added 6 answers

The instantaneous velocity is equal to

f^{'} (\frac{π}{3})

x (t) = t^{2} \sin (t - π)

To find x'(t), use the product rule.

x^{'} (t) = 2 t \sin (t - π) + t^{2} \cos (t - π)

We also know that

y (t) = t \cos t

Again, differentiate with the product rule.

y^{'} (t) = \cos t - t \sin t

The derivative of the entire parametric equation is found as follows:

f^{'} (t) = \frac{y^{'} (t)}{x^{'} (t)} = \frac{\cos t - t \sin t}{2 t \sin (t - π) + t^{2} \cos (t - π)}

Find

f^{'} (\frac{π}{3})

f^{'} (\frac{π}{3}) = \frac{\cos (\frac{π}{3}) - \frac{π}{3} \sin (\frac{π}{3})}{2 (\frac{π}{3}) \sin (\frac{π}{3} - π) + {(\frac{π}{3})}^{2} \cos (\frac{π}{3} - π)}

\approx 0.172261

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