SOLUTION: A particle moves in a straight line so that its velocity v m/s is given by v=9-t^2,where t is the time in seconds, measured from the start of the motion.Find (a) the value of t a

Algebra.Com
Question 1154439: A particle moves in a straight line so that its velocity v m/s is given by v=9-t^2,where t is the time in seconds, measured from the start of the motion.Find
(a) the value of t at which the particle is instantaneously at rest.
(b)the value of t and the speed when the particle is again at its starting point.
(c)the total distance traveled when the particle returns to its starting point.
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.

All these questions relate to Calculus. 

(a)  The particle is instantaneously in rest when its velocity is equal to zero

         v = 0,   i.e.   9 - t^2 = 0.


      It means  t^2 = 9,   t =  = 3 seconds.     ANSWER



(b)  The position (the current coordinate) is ANTI-DERIVATIVE of the speed, i.e.

         position  x =  = 9t - .


     The particle is again at its starting point when its position is zero

          position x = 0,  or  9t -  = 0,  or  27*t- t^3 = 0,   t*(27-t^2) = 0,

          t =  =  seconds = 5.196 second (approx.)     ANSWER


      The speed at this moment is the value of  v = 9 - t^2  at t = , i.e.

      v = 9 -  = 9 - 9*3 = 9 - 27 = -18 meters per second.     ANSWER


RELATED QUESTIONS

A particle moves in a straight line so that its velocity v m/s is given by v=9-t^2,where (answered by ikleyn)
A particle moves in a straight line so that its distance, s m, from a fixed point A on... (answered by Fombitz)
A particle moving in a straight line has initial velocity of 2 m/s at a point O on the... (answered by Shin123,ikleyn)
A particle moves in a straight line so that its distance, s m, from a fixed point A on... (answered by Alan3354)
A particle moves in a straight line so that t seconds its distance from the starting... (answered by Alan3354)
A particle moves in straight line so that t seconds its distance from the starting point... (answered by Alan3354)
A particle moves in a straight line with velocity v(t)=r00t(3t-1)metres per second where... (answered by math_tutor2020)
A particle moves in a straight line with velocity V(t)=root(3t-1) meters per second where (answered by CPhill)
A particle moves in a straight line with velocity v(t)=root(3t-1) metres per second where (answered by math_tutor2020)