2. 09 pointsI Previous Anawers HRW8 4 P.008. An electron\'s position is given by
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Question
2. 09 pointsI Previous Anawers HRW8 4 P.008. An electron's position is given by r 3.00t-7.002 j + 6.00 k, with t in seconds and r in meters. (a) In unit-vector notation, what is the electron's velocity v(t)? (Use the following as necessary: t.) y(t) = | 3.001-14.01 X m/s (b) what is v in unit-vector notation at t = 9.00 s? y(9.00) = m/s (c) What is the magnitude of v att-9.00 s? mys (d) what angle does v make with the positive direction of the x axis at t = 9.00 s? (from the +x axis) The given is a function of time t. Velocity is the time derivative of F. The derivative is taken component by component, and the unit-vector symbols must be retained. The magnitude of a vector is calculated with the Pythagorean with an inverse tangent -10 points HRWB 4.P.008. A plane flies 410 km east from city A to city 8 in 45.0 min and then 900 km south from city B to city C in 1.50 h. (Assume i points east and jpoints north.) (a) In magnitude-angle notation, what is the plane's displacement for the total trip? km 4 (b) In magnitude-angle notation, what is the plane's average velocity for the total trip? km/h (c) What is the plane's average speed for the trip? km/h Submit Answer Save Progress 4. -12 points HRWB 4.P.018. The velocity v of a particle moving in the xy plane is given by v = (6.0t-4.0t2) + 9.0 i, with v in meters per second and t (> 0) is in seconds. (a) What is the acceleration when t 3.0 s? m/si m/s2 5+ m/s2 k (b) When is the acceleration zero? (Enter 'never if appropriate.) (c) When is the velocity zero? (Enter 'never' if appropriate.) (d) When does the speed equal 10 mys? (Enter 'never if appropriate.)Explanation / Answer
Given,
r = 3.00 t i - 7.00 t^2 j + 6.00 k
a)We know from the defination of velocity
v = dr/dt
v = d(3.00 t i - 7.00 t^2 j + 6.00 k)/dt = 3.00t i - 14.00 t j
Hence, v(t) = 3.00 i - 14.00 t j
b)t = 9 s
putting t = 9 in the eqn of velocity obtained in part a
v(9.00) = 3.00 i - 14.00 x 9.00 j
v(9.00) = 3.00 i - 126.00 j
c)v = sqrt (3^2 + 126^2) = 126.036 m/s
Hence, v = 126.036 m
d)theta = tan^-1(-126/3) = -88.64 deg
theta = -88.64 + 180 = 91.36 deg
Hence, theta = 91.36 deg
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