Answer to Question #167406 in Calculus for Rhon

Question #167406

 If 𝑎 = 4𝑡^(− 3/2) , 𝑠 = 16 𝑤ℎ𝑒𝑛 𝑡 = 4, 𝑎𝑛𝑑 𝑠 = 25 𝑤ℎ𝑒𝑛 𝑡 = 6, find the equation of motion 𝑠 = 𝑓(𝑡) and the velocity function 𝑣(𝑡). 


1
Expert's answer
2021-03-01T15:00:58-0500

v(t)=a(t)dt=4t3/2dt=8t+C1v(t)=\int a(t)dt= \int 4t^{-3/2}dt= \frac{-8}{\sqrt{t}} +C_1

s(t)=v(t)dt=(8t0.5+C1)dt=16t+C1t+C2s(t)= \int v(t)dt =\int( -8t^{-0.5}+C_1)dt =-16\sqrt{t} +C_1t + C_2


16=-32+4C1+C2

C2=48+4C1


25=166+6C1+48+4C125=-16 \sqrt{6}+ 6C1+48+4C1

10C1=23+16610C_1=-23+16 \sqrt{6}

C1=1.662.3C_1=1.6 \sqrt{6}-2.3

C2=38.8+6.46C_2=38.8+6.4 \sqrt{6}

Answer: v(t)=8t+1.662.3v(t)= \frac{-8}{\sqrt{t}}+1.6\sqrt{6}-2.3

s(t)=16t+t(1.662.3)+38.8+6.46s(t)=-16\sqrt{t}+t(1.6 \sqrt{6}-2.3) +38.8+6.4\sqrt{6}



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