The position of an object moving along a line is given by $p (t) = 2 t - t^{2} cos (\frac{π}{3} t)$ $p(t) = 2t - t^2cos(( pi )/3t)$ . What is the speed of the object at $t = 5$ $t = 5$ ?

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The position of an object moving along a line is given by $p (t) = 2 t - t^{2} cos (\frac{π}{3} t)$ $p(t) = 2t - t^2cos(( pi )/3t)$ . What is the speed of the object at $t = 5$ $t = 5$ ?

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Answer 1 · 2016-04-21T11:00:51

$p (t) = 2 t - t^{2} cos (\frac{π}{3} t)$ $p(t) = 2t - t^2cos(pi/3t)$

The speed is given as:

$v (t) = . p (t) = 2 + 2 \frac{π}{3} t sin (\frac{π}{3} t)$ $v(t) = dotp(t) = 2+2pi/3tsin(pi/3t)$

so,

$v (5) = 2 + \frac{2 π}{3} \cdot 5 \cdot sin (\frac{5 π}{3}) \approx 2 + \frac{2 π}{3} \cdot 5 \cdot (- 0.87) = - 7.11$ $v(5) = 2+(2pi)/3*5*sin((5pi)/3) ~~ 2 +(2pi)/3*5*(-0.87) = -7.11$

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The position of an object moving along a line is given by $p (t) = 2 t - t^{2} cos (\frac{π}{3} t)$ $p(t) = 2t - t^2cos(( pi )/3t)$ . What is the speed of the object at $t = 5$ $t = 5$ ?

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The position of an object moving along a line is given by p(t)=2t−t2cos(π3t)p(t) = 2t - t^2cos(( pi )/3t) . What is the speed of the object at t=5t = 5 ?

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The position of an object moving along a line is given by $p (t) = 2 t - t^{2} cos (\frac{π}{3} t)$ $p(t) = 2t - t^2cos(( pi )/3t)$ . What is the speed of the object at $t = 5$ $t = 5$ ?