To model a spacecraft, a toy rocket engine is securelyfastened to a 2.00-kg larg

Question

  To model a spacecraft, a toy rocket engine is securelyfastened to a 2.00-kg large puck, which can glide with negligiblefriction over a horizontal surface, taken as the 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?

Explanation / Answer

mass m = 2 kg force F = 8 i - 4t j Accleration a = F / m                      =4 i - 2t j velocity v = integral a dt   with in thelimits t = 0 to t = t                =( 4 i -2t j ) dt with in the limits t = 0 to t =t               = 4t -t^ 2 with in the limits t = 0 to t = t          15 = 4t-t^ 2 t^2 -4t +15 = 0 t = { 4 ±[ 4 ^ 2 + 4(1) ( 15 ) ] } / 2(1) = { 4 ± 8.717 } / 2 = 6.358 s   Since time is positive (b). displacement   S = integral v dt  with the limits t = 0 to t= 6.358                                = integral ( 4t -t ^ 2 )  with the limits t = 0 tot= 6.358                                = [ ( 2t ^ 2 ) - ( t ^ 3 / 3 ) ] with the limits t = 0to t= 6.358                                = 80.84 - 85.67                                = -4.82 m

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