# math

posted by .

Given the position function s = 4t^3 − 24t^2 + 6t + 6.

find s and v when a = 0

(Where v is the velocity and a is the acceleration.).

• math -

v= ds/dt=12t^2-48t+6
a= dv/dt=24t-48=0 so t=2

find s, v when t=2

• math -

so i just have to sub t=2 in
v = 12t^2-48t+6 to get v and
s = 4t^3-24t^2+6t+6 to get s ?

## Similar Questions

1. ### Calculus

A particle moves on a vertical line. Its position, s, in metres at t seconds is given by s(t) = t^3 - 9t^2 + 24t, t>0/ I found the velocity and acceleration functions. s'(t) = 3t^2 - 18t + 24 s''(t) = 6t-18 b) When is the particle …
2. ### calculus

5. A particle moves along the x-axis in such a way that its position at time t is given by x=3t^4-16t^3+24t^2 for -5 ≤ t ≤ 5. a. Determine the velocity and acceleration of the particle at time t. b. At what values of t …
3. ### calculus

A point moving on a coordinate line has position function s. Find the velocity and acceleration at the t, and describe the motion of the point during the indicated time interval s(t)=-2t^3+15t^2-24t-6 [0,5]
4. ### Calculus

The position of a particle moving on a horizontal line is given by s(t)=2t^3-15t^2+24t-5, where s is measured in feet and t in seconds. a: What is the initial position of the particle?
5. ### Brief Calculus

The position s of a point (in feet) is given as a function of time t (in seconds). s = −10 + t − 15t2;  t = 8 (a) Find the point's acceleration as a function of t. s''(t)= I know this answer, it is -30 (b) Find the …
6. ### Physics

Automotive engineers refer to the time rate of change of acceleration as the "jerk." Assume an object moves in one dimension such that its jerk J is constant. (a) Determine expressions for its acceleration ax(t), velocity vx(t), and …
7. ### math

The position function of a particle in rectilinear motion is given by s(t) s(t) = t3 – 9t2 + 24t + 1 for t ≥ 0. Find the position and acceleration of the particle at the instant the when the particle reverses direction. Include …
8. ### Calculus

The position function of a particle in rectilinear motion is given by s(t) s(t) = t^3 - 9t^2 + 24t + 1 for t ≥ 0. Find the position and acceleration of the particle at the instant the when the particle reverses direction. Include …
9. ### calc

An object has a constant acceleration of 30 ft/sec2, an initial velocity of −10 ft/sec, and an initial position of 4 ft. Find the position function, s(t), describing the motion of the object.
10. ### Calculus

Find the velocity and position vectors of a particle that has the given acceleration and the given initial velocity and position. a(t) = 2 i + 6t j + 12t2 k, v(0) = i, r(0) = 2 j − 7 k

More Similar Questions