A particle moves on a line so that its distance from the origin at time t s is x m and its velocity is v m/s.
i) The acceleration satisfies (d^2 x)/(dt^2) = n^2 (3 – x) where n is a constant, and the particle is released from rest at x = 0.
a) Show that ½ v^2 – n^2 (3x – ½ x^2) = 0
b) Hence, show that the particle never moves outside a certain interval.
ii) If the maximum speed is 10 m/s, what is the period of the motion?
I got i) a) and I think I got ii), but I would really appreciate help with i) b) and part ii)
Thanks
i) The acceleration satisfies (d^2 x)/(dt^2) = n^2 (3 – x) where n is a constant, and the particle is released from rest at x = 0.
a) Show that ½ v^2 – n^2 (3x – ½ x^2) = 0
b) Hence, show that the particle never moves outside a certain interval.
ii) If the maximum speed is 10 m/s, what is the period of the motion?
I got i) a) and I think I got ii), but I would really appreciate help with i) b) and part ii)
Thanks