The position of a particle moving along a coordinate line is s equals StartRoot 92 plus 4 t EndRoot , with s in meters and t in seconds. Find the particle's velocity and acceleration at t equals 2 sec.

Velocity = 0.2m/s

Acceleration = - 10m/s²

Step-by-step explanation:

Since S = sqrt (92 + 4t)

Differentiate S wrt t,

Velocity V = dS/dt = 2/sqrt (92 + 4t)

When t = 2s

V = 2/sqrt (92 + 4*2) = 2/sqrt (100)

V = 2/10 = 0.2 m/s

For acceleration a,

Differentiate V wrt t,

a = dV/dt = (-92-4t) / sqrt (92+4t)

At t = 2s

a = - 100/sqrt (100) = - 100/10

a = - 10 m/s²