Question

A particle moves so that its position as a function of time in SI units is r = i + (3.0) t2 j + t k. Write expressions for its velocity and its acceleration as functions of time. Evaluate for t = 5.1 s. i-component of velocity?

Answer 1

Answer:

i - component of V is zero for any value of t  i-e  no motion in this direction

Explanation:

Since

r= i+3$t^{2}$j+t k

==> V = $\frac{d r}{dt}$=$\frac{d(i+3t^{2}j+kt) }{dt}$

=$6tj+k$

and acceleration is given by taking derivative of velocity w.r.t  t

==> a= $\frac{dV}{dt}$=$\frac{d(6tj+k)}{dt}$=$6j$

so, V=0i+6tj+k

and

a = 0i+6j+k

i - component of V is zero for any value of t  i-e  no motion in this direction