Question

The function gives the distances (in feet) traveled in time t (in seconds) by a particle. Find the velocity and acceleration at the given time.
s = 6t3 + 6t2 + 8t + 3, t = 3
Possible answers
v = 36 ft/s, a = 90 ft/s2
v = 120 ft/s, a = 206 ft/s2
v = 90 ft/s, a = 36 ft/s2
v = 206 ft/s, a = 120 ft/s2

Answer 1

Answer:

v=206ft/s , a=120ft/s

Step-by-step explanation:

We are given the equation of displacement

$S = 6t^3 + 6t^2 + 8t + 3,$

• velocity = ds/dt

        upon differentiating the given equation

        ds/dt = $18t^2 + 12t + 8$

        upon substituting t = 3

         v = 206ft/s

• Acceleration

          a= dv/dt

          upon differentiating

          dv/dt = 36t + 12

          put t= 3

          a=120ft/s