The position vector of a particle R→ as a function of time is given by R→$$=4sin(2$$$$π$$$$t)i^+4cos(2$$$$π$$$$t)j^Where$$ R is in meters, t is in seconds and $$i^$$ and $$j^$$ denote unit vectors along $$x-and$$ $$y-directions$$, respectively. Which one of the following statements is wrong for the motion of particle?

Question

The position vector of a particle R→ as a function of time is given by R→$$=4sin(2$$$$π$$$$t)i^+4cos(2$$$$π$$$$t)j^Where$$ R is in meters, t is in seconds and $$i^$$ and $$j^$$ denote unit vectors along $$x-and$$ $$y-directions$$, respectively. Which one of the following statements is wrong for the motion of particle?

Infinity Learn · Accepted Answer

Here, R→$$=4sin(2$$$$π$$$$t)i^+4cos(2$$$$π$$$$t)j^The$$ velocity of the particle isv→$$=dR$$→$$dt=ddt$$[$$4sin(2$$$$π$$$$t)i^+4cos(2$$$$π$$$$t)j^$$]$$=8$$$$π$$$$cos$$$$(2$$$$π$$$$t)i^-8$$$$π$$$$sin$$$$(2$$$$π$$$$t)j^its$$ magnitude is|v→|$$=(8$$$$π$$$$cos$$$$(2$$$$π$$$$t))2+(-8$$$$π$$$$sin$$$$(2$$$$π$$$$t))2=64$$$$π$$$$2cos2(2$$$$π$$$$t)+64$$$$π$$$$2sin2(2$$$$π$$$$t)=64$$$$π$$$$2cos2(2$$$$π$$$$t)+sin2(2$$$$π$$$$t)=64$$$$π$$$$2$$                                        as $$sin2$$θ$$+cos2$$θ$$=1=8$$$$π$$$$m/s$$

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The position vector of a particle R→ as a function of time is given by R→=4sin(2πt)i^+4cos(2πt)j^Where R is in meters, t is in seconds and i^ and j^ denote unit vectors along x-and y-directions, respectively. Which one of the following statements is wrong for the motion of particle?

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