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CALC A remote-controlled car is moving in a vacant parking

Chapter 6, Problem 8E

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QUESTION:

A remote-controlled car is moving in a vacant parking lot. The velocity of the car as a function of time is given by \(\vec{v}=\left[5.00 \mathrm{~m} / \mathrm{s}-\left(0.0180 \mathrm{~m} / \mathrm{s}^{3}\right) t^{2}\right] \hat{\boldsymbol{\imath}}+\left[2.00 \mathrm{~m} / \mathrm{s}+\left(0.550 \mathrm{~m} / \mathrm{s}^{2}\right) t\right] \hat{\boldsymbol{j}}\)

(a) What are \(a_{x}(t)\) and \(a_{y}(t)\), the x- and y-components of the velocity of the car as functions of time?

(b) What are the magnitude and direction of the velocity of the car at t = 8.00 s?

(c) What are the magnitude and direction of the acceleration of the car at t = 8.00 s?

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QUESTION:

A remote-controlled car is moving in a vacant parking lot. The velocity of the car as a function of time is given by \(\vec{v}=\left[5.00 \mathrm{~m} / \mathrm{s}-\left(0.0180 \mathrm{~m} / \mathrm{s}^{3}\right) t^{2}\right] \hat{\boldsymbol{\imath}}+\left[2.00 \mathrm{~m} / \mathrm{s}+\left(0.550 \mathrm{~m} / \mathrm{s}^{2}\right) t\right] \hat{\boldsymbol{j}}\)

(a) What are \(a_{x}(t)\) and \(a_{y}(t)\), the x- and y-components of the velocity of the car as functions of time?

(b) What are the magnitude and direction of the velocity of the car at t = 8.00 s?

(c) What are the magnitude and direction of the acceleration of the car at t = 8.00 s?

ANSWER:

Step 1 of 4

Given data:

The velocity of the car as a function of time is:

\(\vec v = \left[ {5.00{\rm{\;m/s}} - \left( {0.0180{\rm{\;m/}}{{\rm{s}}^{\rm{3}}}} \right){t^2}} \right]\hat i + \left[ {2.00{\rm{\;m/s}} + \left( {0.550{\rm{\;m/}}{{\rm{s}}^2}} \right)t} \right]\hat j\)

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