Answer:
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
Answer:
(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
