csat-suneung 2020 Q10

csat-suneung · South-Korea · csat__math-science 3 marks Applied differentiation Kinematics via differentiation

A point P moving on the coordinate plane has position $( x , y )$ at time $t \left( 0 < t < \frac { \pi } { 2 } \right)$ given by
$$x = t + \sin t \cos t , \quad y = \tan t$$
What is the minimum speed of point P for $0 < t < \frac { \pi } { 2 }$? [3 points]
(1) 1
(2) $\sqrt { 3 }$
(3) 2
(4) $2 \sqrt { 2 }$
(5) $2 \sqrt { 3 }$

A point P moving on the coordinate plane has position $( x , y )$ at time $t \left( 0 < t < \frac { \pi } { 2 } \right)$ given by

$$x = t + \sin t \cos t , \quad y = \tan t$$

What is the minimum speed of point P for $0 < t < \frac { \pi } { 2 }$? [3 points]\\
(1) 1\\
(2) $\sqrt { 3 }$\\
(3) 2\\
(4) $2 \sqrt { 2 }$\\
(5) $2 \sqrt { 3 }$

Paper Questions

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