1. To model a spacecraft, a toy rocketengine is securely fastened to a 2.00-kg l

Question

1.     To model a spacecraft, a toy rocketengine is securely fastened to a 2.00-kg large puck, which canglide with negligible friction over a horizontal surface, taken asthe xy plane. The engine exerts a time-dependent force, F= (8.00 î– 4.00tj) N, wheret is in seconds, on the puck. If the puck is initially atrest, (a) At what time will it be moving with a speed of 15.0 m/s?(b) How far is the puck from its initial position when its speed is15.0 m/s? (c) Through what total displacement has the puck traveledat this time?

If you do this by breaking F intoit's components and then solving for the acceleration componentsyou should get 4.00 m/s^2 and -2.00*t m/s^2 correct? Then shouldn'tyou set 15.0 m/s = (4.00-2.00t)*t to find time? What am Imissing since this doesn't work?

Explanation / Answer

acceleration a(t) = (4.00 i - 2.00*tj) m/s2 velocity v(t) = a(t) dt = (4.00*t i - t2 j)m/s position r(t) = v(t) dt =(2.00*t2 i -t3/3 j) m a) speed v = [4.00*t)2+ t4]= 15 16t2 + t4 = 225 (t2 - 9)(t2 + 25) = 0 t = 3 s b) r(3) = (18 i - 9 j) m magnitude = (182 + 92) = 20.1 m c) displacement = (18 i - 9 j) m

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