Question

S=3-2t+3t^2

What is the instantaneous velocity and it’s acceleration at t=3s
At what time is the particle at rest

Answer 1

Step-by-step explanation:

Given:

X(t) = 3 - 2*t + 3*t²

t = 3 s

_______________

V(t) - ?

a(t) - ?

Speed is the first derivative of the coordinate, acceleration is the second.

1)

V(t) = X' = (3 - 2*t + 3*t²)' = 0 - 2 +6*t = 6*t - 2

V(3) = 6*3 - 2 = 16 m/s

2)

a(t) = X'' = V' = (6*t - 2)' = 6 m/s²

a(3) = 6 m/s²

3)

The body will stop (V = 0 ) in (t) seconds:

V(t) = 6*t - 2

0 = 6*t - 2

6*t = 2

t = 2/6 = 1/3 ≈ 0,33 s