An object's two dimensional velocity is given by $v (t) = (t^{3}, t - t^{2} sin (\frac{π}{8}) t)$ $v(t) = ( t^3, t-t^2sin(pi/8)t)$ . What is the object's rate and direction of acceleration at $t = 3$ $t=3$ ?

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An object's two dimensional velocity is given by $v (t) = (t^{3}, t - t^{2} sin (\frac{π}{8}) t)$ $v(t) = ( t^3, t-t^2sin(pi/8)t)$ . What is the object's rate and direction of acceleration at $t = 3$ $t=3$ ?

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Answer 1 · 2017-04-01T15:53:05

The rate of acceleration is $= 27.63 m s^{- 1}$ $=27.63ms^-1$ in the direction of $= 167.69$ $=167.69$ º

Explanation:

The velocity is

$v (t) = (t^{3}, t - t^{2} sin ((\frac{π}{8}) t))$ $v(t)=(t^3,t-t^2sin((pi/8)t))$

Acceleration is the first derivative of the velocity

$a (t) = \frac{d v (t)}{d t} = (3 t^{2}, 1 - 2 t sin (\frac{π}{8}) t - t^{2} (\frac{π}{8}) cos (\frac{π}{8}) t)$ $a(t)=(dv(t))/dt=(3t^2,1-2tsin(pi/8)t-t^2(pi/8)cos(pi/8)t)$

When $t = 3$ $t=3$

$a (3) = \frac{d v (3)}{d t} = (27, 1 - 6 sin (\frac{3}{8} π) - (\frac{9}{8} π) cos (\frac{3}{8} π))$ $a(3)=(dv(3))/dt=(27,1-6sin(3/8pi)-(9/8pi)cos(3/8pi))$

$= (27, 1 - 5.54 - 1.35)$ $=(27,1-5.54-1.35)$

$= (27, - 5.89)$ $=(27,-5.89)$

The object rate of acceleration is

$= \sqrt{(27^{2}) + {(- 5.89)}^{2}}$ $=sqrt((27^2)+(-5.89)^2)$

$= 27.63 m s^{- 2}$ $=27.63ms^-2$

The direction is

$= arctan (- \frac{5.89}{27})$ $=arctan(-5.89/27)$

The angle is in the 2nd quadrant and is

$= 167.69$ $=167.69$ º

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An object's two dimensional velocity is given by $v (t) = (t^{3}, t - t^{2} sin (\frac{π}{8}) t)$ $v(t) = ( t^3, t-t^2sin(pi/8)t)$ . What is the object's rate and direction of acceleration at $t = 3$ $t=3$ ?

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Explanation:

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An object's two dimensional velocity is given by v(t) = ( t^3, t-t^2sin(pi/8)t)v(t)=(t3,t−t2sin(π8)t)v(t) = ( t^3, t-t^2sin(pi/8)t). What is the object's rate and direction of acceleration at t=3 t=3t=3 ?

1 Answer

Explanation:

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An object's two dimensional velocity is given by $v (t) = (t^{3}, t - t^{2} sin (\frac{π}{8}) t)$ $v(t) = ( t^3, t-t^2sin(pi/8)t)$ . What is the object's rate and direction of acceleration at $t = 3$ $t=3$ ?