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
"(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"
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