Question

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

Answer 1

$(a) Position = R(t) = t² i + t³ j + 3t k$

$(b) Velocity, V(t)= \frac{dR(t)}{dt} = 2ti+3t²j+3k$

$(c) Speed = |v(t)| = \sqrt{(2t)²+(3t²)²+3²}$

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

When $t = 1$

$(a) Position = 1²i+1³j+3(1)k = i+j+3k$

$(b) Velocity = 2(1)i+3(1)²j+3k = 2i+3j+3k$

$(c) Speed = \sqrt{(2(1))²+(3(1)²)²+3²} = \sqrt{4+9+9} = \sqrt{22}$

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