The position of an electron is given by r = (5.0) t i + (-5.0) t2 j+ (2.0) k (wh

Question

The position of an electron is given by r = (5.0) t i + (-5.0) t2 j+ (2.0) k (where t is in seconds and the coefficients have the proper units for r to be in meters). What is v(t) for the electron? a)What is its distance from the origin at t = 1.8 s? b)In unit-vector notation, what is v at t = 1.8 s? i-component of velocity? c)j-component of velocity? d)k-component of velocity? e)What is the magnitude of v just then? f)What is the direction of v just then?

Explanation / Answer

v(t)= 5 i- 10*t j a) r(1.8)=5*1.8 i-5*1.8^2 j+2 k=9 i-16.2 j+2 k distance from origin =18.63 m b) V(t) is always constant = 5 m/s @ t = 1.8 s unit vector = 0.27 m/s in i direction c) j component of velocity @ t= 1.8 s => -18 j m/s d) k component of velocity => 0m/s e) magnitude of velocity = sqrt (5^2 + 18^2 ) = 18.7 m/s f) tan(theta) = Vv / Vx = -18 / 5 theta = 105.5 degree from x-axis

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