A particle moves so that its position (in meters) as a function of time (in seconds) is r = i ^ + 4t2 j ^ + tk ^. Write expressions for (a) its velocity and (b) its acceleration as functions of time.

a.V=8tj+k

b.a=8j

Explanation:

Given:

Position r= i+4t^2j +tk

Nb r is position in metre and time in seconds

a.velocity is change in position/ change in time

v= ∆r/∆t =dr/dt

V=d ( i+ 4t^2j+tk)/dr

Differenting with respect to (t)

V=8tj+K

b.acceleration = change in velocity/change in time

a= ∆v/∆r =dv/dt

a=d (8tj+k)/dt

a= 8j

(a) velocity, v = 8t j + k

(b) acceleration, a = 8 j

Explanation:

The position of the particle as a function of time is given as;

r = i + 4t² j + t k         (i)

(a) To get the expression of its velocity, v, find the derivative of its position with respect to time by differentiating equation (i) with respect to t as follows;

v = dr / dt = 0 + 8t j + k

v = dr / dt = 8t j + k

v = 8t j + k          (ii)

Therefore, the equation/expression for the particle's velocity (v) is

v = 8t j + k

(b) To get the expression of its acceleration, a, find the derivative of its velocity with respect to time by differentiating equation (ii) with respect to t as follows;

a = dv / dt = t j + 0

a = dv / dt = t j

a = 8 j

Therefore, the expression for the particle's acceleration, a, is a = 8 j

unlike poles attract

force required to detach it is given by

charges are taken to be fundamental charge

now we have

so above is the minimum distance at which it will detach