A rabbit runs across a parking lot on which a set of coordinate axes has, strangely enough, been drawn.
The coordinates (meters) of the rabbit's position as function of time t(seconds) are given by

$x (t) = - \frac{t^{2}}{2} + 5 t + 20$
And $y (t) = t^{2} - 10 t + 30$

Find the velocity at time t = 15s.

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Solution

The correct option is C

$x = - \frac{t^{2}}{2} + 5 t + 20, y = t^{2} - 10 t + 30$
Let the x component of velocity be $v_{x}$ and y component $v_{y}$
$∴ v_{x} = \frac{d x}{d t} = - \frac{2 t}{2} + 5 = - t + 5$
$v_{y} = \frac{d y}{d t} = 2 t - 10$
At t= 15s
$v_{x} = - 15 + 5 = - 10, v_{y} = 2 (15) - 10 = 20$ .
$∴ \to v = - 10^i + 20^j$

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A rabbit runs across a parking lot on which a set of coordinate axes has, strangely enough, been drawn.
The coordinates (meters) of the rabbit's position as function of time t(seconds) are given by

$x (t) = - \frac{t^{2}}{2} + 5 t + 20$
And $y (t) = t^{2} - 10 t + 30$

Find the velocity at time t = 15s.

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A rabbit runs across a parking lot on which a set of coordinate axes has, strangely enough, been drawn.
The coordinates (meters) of the rabbit's position as functions of time t (seconds) are given by

$x=-{t^2\over 2}+5t+20$
And $y=t^2-10t+30$

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A rabbit runs across a parking lot on which a set of coordinate axes has, strangely enough, been drawn.
The coordinates (meters) of the rabbit's position as functions of time t (seconds) are given by

$x = - \frac{t^{2}}{2} + 5 t + 20$
And $y = t^{2} - 10 t + 30$

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A rabbit runs across a parking lot on which a set of coordinate axes has, strangely enough, been drawn.
The coordinates(meters) of the rabbit's position as function of time t(seconds) are given by

$x (t) = - \frac{t^{2}}{2} + 5 t + 20 A n d y (t) = t^{2} - 10 t + 30$

(a)At t=10s, what is the rabbot's position vector $\to r$ in unit-vector notation and in magnitude-angle notation?

A rabbit runs across a parking lot on which a set of coordinate axes has, strangely enough, been drawn.
The coordinates(meters) of the rabbit's position as function of time t(seconds) are given by

$x (t) = - \frac{t^{2}}{2} + 5 t + 20 A n d y (t) = t^{2} - 10 t + 30$

(a)At t=10s, what is the rabbot's position vector $\to r$ in unit-vector notation and in magnitude-angle notation?

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A rabbit runs across a parking lot on which a set of coordinate axes has, strangely enough, been drawn. The coordinates (meters) of the rabbit's position as function of time t(seconds) are given by x(t)=−t22+5t+20 And y(t)=t2−10t+30 Find the velocity at time t = 15s.

The correct option is C x=−t22+5t+20, y=t2−10t+30 Let the x component of velocity be vx and y component vy ∴ vx=dxdt=−2t2+5=−t+5 vy=dydt=2t−10 At t= 15s vx=−15+5=−10,vy=2(15)−10=20. ∴→v=−10^i+20^j