Question

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.

Answer 1

Answer:

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