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

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

Step-by-step explanation:

Since

r= i+3
`t^(2)`j+t k

==> V =
`(d r)/(dt)`=
`(d(i+3t^(2)j+kt) )/(dt)`

=
`6tj+k`

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

==> a=
`(dV)/(dt)`=
`(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