Problem 12.28 Two particles A and B start from rest at the origin s 0 and move a
ID: 1572330 • Letter: P
Question
Problem 12.28 Two particles A and B start from rest at the origin s 0 and move along a straight line such that aA (6t 3) ft/s2 and aB (6t2 4) ft/s?, where t is in seconds. Part A Determine the distance between them when 7 s. Express your answer using three significant figures and include the appropriate units. AB Value ft Submit My Answers Give Up incorrect; Try Again; 5 attempts remaining Part B Determine the total distance particle A has traveled in 7 s. Express your answer using three significant figures and include the appropriate units. SA total a Value Units Submit My Answers Give Up Part C Determine the total distance particle B has traveled int 7 s.Explanation / Answer
A)
for particle A :
aA = 6t - 3
dVA/dt = 6t - 3
VA = 3t2 - 3t
displacement is given as
dxA /dt = = 3t2 - 3t
xA = t3 -1.5 t2
at t = 7 s
xA = 73 -1.5 72 = 269.5
for particle B :
aB = 6t2 - 4
dVB/dt = 6t2 - 4
VB = 2t3 - 4t
displacement is given as
dxB /dt = 2t3 - 4t
xB = (0.5)t4 - 2 t2
at t = 7 s
xB = (0.5) (7)4 - 2 (7)2= 1102.5 ft
distance between A and B at t = 7 is given as
D = xB - xA = 1102.5 - 269.5 = 833 ft
Part B
xA = 73 -1.5 72 = 269.5
part C
xB = (0.5) (7)4 - 2 (7)2= 1102.5 ft