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CALC A remote-controlled car is moving in a vacant parking
Chapter 6, Problem 8E(choose chapter or problem)
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?
Questions & Answers
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:
\(\vec v = \left[ {5.00{\rm{\;m/s}} - \left( {0.0180{\rm{\;m/}}{{\rm{s}}^{\rm{3}}}} \right){t^2}} \right]\hat i + \left[ {2.00{\rm{\;m/s}} + \left( {0.550{\rm{\;m/}}{{\rm{s}}^2}} \right)t} \right]\hat j\)