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Answer: CALC A web page designer creates an animation in
Chapter 3, Problem 3E(choose chapter or problem)
A web page designer creates an animation in which a dot on a computer screen has a position of \(\vec{r}=\left[4.0 \mathrm{~cm}+\left(2.5 \mathrm{~cm} / \mathrm{s}^{2}\right) t^{2}\right] \hat{\imath}+(5.0 \mathrm{~cm} / \mathrm{s}) t \hat{\jmath}\)
(a) Find the magnitude and direction of the dot’s average velocity between \(t=0 \text { and } t=2.0 \mathrm{~s} \text {. }\).
(b) Find the magnitude and direction of the instantaneous velocity at \(t=0, t=1.0 \mathrm{~s}, \text { and } t=2.0 \mathrm{~s}\).
(c) Sketch the dot’s trajectory from \(t=0\) to \(t=2.0 \mathrm{~s}\), and show the velocities calculated in part (b).
Questions & Answers
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QUESTION:
A web page designer creates an animation in which a dot on a computer screen has a position of \(\vec{r}=\left[4.0 \mathrm{~cm}+\left(2.5 \mathrm{~cm} / \mathrm{s}^{2}\right) t^{2}\right] \hat{\imath}+(5.0 \mathrm{~cm} / \mathrm{s}) t \hat{\jmath}\)
(a) Find the magnitude and direction of the dot’s average velocity between \(t=0 \text { and } t=2.0 \mathrm{~s} \text {. }\).
(b) Find the magnitude and direction of the instantaneous velocity at \(t=0, t=1.0 \mathrm{~s}, \text { and } t=2.0 \mathrm{~s}\).
(c) Sketch the dot’s trajectory from \(t=0\) to \(t=2.0 \mathrm{~s}\), and show the velocities calculated in part (b).
ANSWER:
Step 1 of 4
The position vector of the dot on the screen is given as:
\(\vec r = \left[ {4.0\;{\rm{cm}} + \left( {2.5\;{\rm{cm/}}{{\rm{s}}^{\rm{2}}}} \right){t^2}} \right]\hat i + \left( {5.0\;{\rm{cm/s}}} \right)t\hat j\)
The position of dot is in 2-D plane, the derivative of that position with respect to the time will give the velocity of the dot and the velocity will contain two components, one in x-direction and another in y-direction.
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