Answer to Question #262382 in Calculus for Spart

Question #262382

Consider a moving body B whose position at time t is given by R(t)=t2 i+t3 j+3 tk .

[Then V (t) = dR(t) / dt and A(t) = dV (t)/dt denote, respectively, the velocity and acceleration of B.]

When t = 1, find for the body B:

(a) position (b) velocity v (c) speed s (d) acceleration a


1
Expert's answer
2021-11-08T16:45:28-0500

"(a) Position = R(t) = t\u00b2 i + t\u00b3 j + 3t k"

"(b) Velocity, V(t)= \\frac{dR(t)}{dt} = 2ti+3t\u00b2j+3k"

"(c) Speed = |v(t)| = \\sqrt{(2t)\u00b2+(3t\u00b2)\u00b2+3\u00b2}"


"(d) Acceleration, A(t)= \\frac{dV(t)}{dt} = 2i + 6tj"


When "t = 1"


"(a) Position = 1\u00b2i+1\u00b3j+3(1)k = i+j+3k"


"(b) Velocity = 2(1)i+3(1)\u00b2j+3k = 2i+3j+3k"


"(c) Speed = \\sqrt{(2(1))\u00b2+(3(1)\u00b2)\u00b2+3\u00b2} = \\sqrt{4+9+9} = \\sqrt{22}"


"(d) Acceleration = 2i + 6(1)j = 2i+6j"






Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!

Leave a comment

LATEST TUTORIALS
New on Blog
APPROVED BY CLIENTS