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 π‘₯ = 5𝑑 3 βˆ’105𝑑 where π‘₯ is in inches and 𝑑 is in seconds. When 𝑑 = 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 𝑑 = 0, determine its total velocity when 𝑑 = 4 𝑠.


Answer: 𝒗 = πŸπŸ–. πŸ•πŸ“ 𝒇𝒕/s


1
Expert's answer
2021-02-25T04:15:15-0500

Total acceleration , a⃗=axi+ayj=30ti+ayj\vec{a}=a_x{i}+a_y{j}=30t{i}+a_y{j}

aβƒ—=900t2+ay2;t=2β€…β€ŠβŸΉβ€…β€Š75=900βˆ—22+ay2β€…β€ŠβŸΉβ€…β€Šay=45in/s2\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

a⃗=[30ti+45j]in/s2\vec{a}=[30t{i}+45{j}] in/s^2

Velocity at t=4 sec β€…β€ŠβŸΉβ€…β€Švβƒ—=uβƒ—+aβƒ—t=βˆ’105i+[(30βˆ—4)i+45j]βˆ—4\implies \vec{v}=\vec{u}+\vec{a}t=-105i+ [(30*4){i}+45{j}]*4

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

∣vβˆ£βƒ—=3752+1802=415.96in/s=415.96in/s2=34.66ft/s2\vec{|v|}=\sqrt{375^2+180^2}=415.96 in/s=415.96in/s^2=34.66 ft/s^2


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