Question

The position (in meters) of a particle moving in a
straight line is given by s(t) = ^2 + 8t + 18, where t
is measured in seconds. What is the instantaneous
velocity of the particle at t = 12 seconds​

Answer 1

Given :-

Position of Particle = S = t² + 8t + 18

Here, we will differentiate 's' w.r.t 't' then we will get velocity.

V = ds/dt

V = d(t²+8t+18)/dt

V = 2t + 8 (xⁿ = nxⁿ-¹) ------(1)

Putting the value t = 12 in above equation.

V = 2(12) + 8

V = 32 ms-¹

Hence,

The velocity of particle = V = 32 ms-¹.