# Answer to Question #166089 in Mechanical Engineering for John Patrick

Question #166089

A particle has such a curvilinear motion that its x coordinate is defined by 𝑥 = 5𝑡 3 −105𝑡 where 𝑥 is in inches and 𝑡 is in seconds. When 𝑡 = 2 𝑠, the total acceleration is 75 𝑖𝑛/𝑠 2 . If the y component of acceleration is constant and the particle starts from rest at the origin when 𝑡 = 0, determine its total velocity when 𝑡 = 4 𝑠.

Answer: 𝒗 = 𝟏𝟖. 𝟕𝟓 𝒇𝒕/s

1
2021-02-25T04:15:15-0500

Total acceleration , "\\vec{a}=a_x{i}+a_y{j}=30t{i}+a_y{j}"

"\\vec{a}= \\sqrt{900t^2+a_y^2}; t=2 \\implies75=\\sqrt{900*2^2+a_y^2} \\implies a_y=45 in\/s^2"

"\\vec{a}=[30t{i}+45{j}] in\/s^2"

Velocity at t=4 sec "\\implies \\vec{v}=\\vec{u}+\\vec{a}t=-105i+ [(30*4){i}+45{j}]*4"

"\\vec{v}=[375{i}+180{j}]in\/s"

"\\vec{|v|}=\\sqrt{375^2+180^2}=415.96 in\/s=415.96in\/s^2=34.66 ft\/s^2"

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