1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Total distance covered .

  1. Mar 19, 2016 #1
    1. The problem statement, all variables and given/known data
    The displacement vector of a particle of mass 50 gm. is given as a function in time (t) by the relation ##\vec S##=(5t-t2) ##\hat c## where ##\hat c## is a constant unit vector , s is measured in centimetre and t in second .Knowing that the particle started its motion at t=0
    Find :
    (1) The force vector acting on the particle and the work done by this force during the first five seconds of motion.
    (2) The total distance covered during the first three seconds of motion.
    2. Relevant equations
    ##w=\vec F \cdot \vec S##
    3. The attempt at a solution
    The requirement number (1) is quite easy by differentiating vector s with respect to time 2 times we get the acceleration vector and we already have the mass , so we can get the force easily, but the problem is in getting the total distance covered , in my best attempt , I could only get the maximum displacement by differentiating vector s with respect to time and equal it with zero we will get 5-2t=0 so displacement is maximum when t=2.5 seconds , what should I do next ?
  2. jcsd
  3. Mar 19, 2016 #2

    Buzz Bloom

    User Avatar
    Gold Member

    Hi Nadar:

    What is the displacement at t=0?
    What is the displacement at t=3?
    How far did it move between t=0 and t=3?

    Hope this helps.

  4. Mar 19, 2016 #3


    User Avatar

    Staff: Mentor

    I think you want to investigate the arc length of a curve. The curve in this case is one dimensional (lies along a straight line), can you think of a way to sum up the distance over time?
  5. Mar 21, 2016 #4
    Thanks , The problem is with the distance not the displacement .
  6. Mar 21, 2016 #5
    Nope .
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted