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
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-> 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
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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):
(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
