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 moving up? down?

c) Find the distance the particle travels between t=0 and t=6.

  1. 👍 0
  2. 👎 0
  3. 👁 152
asked by Alex
  1. Right on the first.
    Now when it is going up> When is s'positive? When is it negative? The sign of s'is direction. Hint: factor the quadratic and test domains to see when it is +-

    The distance it travels? Integrate velocity over time. The area under a velocity time graph is distance.

Respond to this Question

First Name

Your Response

Similar Questions

  1. math

    A particle travelling along a straight line starts with a velociry ofu metres per second and its speed increases per second by rl metres. The particle travels 10 metres in 2 seconds and 28 metres in 4 seconds. Find u and a. (lf

    asked by noushil on November 28, 2015
  2. math

    For 4.95 seconds , a particle moves in a straight line according to the position function: s(t) = e^t(5-t)-5 . a. when id the particle at rest ? when is particle moving forward ? b. Find the total distance traveled by the particle

    asked by Anonymous on November 7, 2013
  3. math

    For 4.95 seconds , a particle moves in a straight line according to the position function: s(t) = e^t(5-t)-5 . a. when id the particle at rest ? when is particle moving forward ? b. Find the total distance traveled by the particle

    asked by Anonymous on November 7, 2013
  4. calculus

    a particle moves along a number line measured in cm so that its position at time t sec is given by s=72/(t+2) +k, k is a constant and t>=0 seconds. (a) Find the instantaneous velocity of the particle at t=4 seconds (b) Find the

    asked by nadra on February 4, 2011
  5. calculus

    the position of a particle moving along a coordinate line is s=√(1+4t) , with s in metres and t in seconds. Find the particle's velocity and acceleration at t=6 sec

    asked by zizi on November 4, 2014
  6. kinematics

    these are two similar kinematics maths question which i don't know. Please help! 1)A particle moves in a straight line so that its distance, s metres, from a fixed point O is given by s = 2t^3 - 3t^2 - 12t + 6, where t is the time

    asked by zachary on June 19, 2009
  7. calculus

    A particle moves in a straight line with velocity given by v(t) =sin t metres per second. Find the total distance travelled by the particle in the first 4 seconds of motion

    asked by jenna on February 14, 2012
  8. Physics

    A particle moves in a straight line so that its position (x cm) from a fixed point O at time (t seconds) is given by x= t^3-6t^2-15t-5 Find the average speed of the particle in the first 7 seconds

    asked by Jane on September 8, 2012
  9. AP CALC. AB

    1.The position of a particle moving on the line y = 2 is given by x(t)= 2t^3-13t^2+22t-5 where t is time in seconds. When is the particle at rest? a. t =0.268, 2.500, and 3.732 b. t = 0, 1.153, and 3.180 c. t = 1.153, 2.167 and

    asked by Rachel on October 12, 2014
  10. Calculus

    Given the position function, s(t)= (-t^3/3)+(13t^2 /2)-30t, between t=0 and t = 9, where s is given in feet and t is measured in seconds, find the interval in seconds where the particle is moving to the right. a) 3 < t < 9 b) 5 <

    asked by Alice on February 1, 2019

More Similar Questions