# Accelerated Linear Motion

Hey
Im having some trouble with this Accelerated Linear Motion question. I dont have any clue where i should even start with part (B).
(A) A particle moving in a straight line with constant acceleration passes three points, p, q and r and has speeds u and 7u and p and r respecitively.
(I) Find its speed at q, the midpoint of pr, in terms o u
(II)Show that the time from p to q is twice that from q to r
(B) A juggler throws up six balls, one after the other at equal intervals of time t, each to a height of 3m. The first ball returns to his hand t seconds after the sixth was thrown up and is immediately thrown to the same height, and so on continually. You may assume that each ball moves vertically.
Find:
(i) the initial velocity of each ball
(ii) the time t
(iii) the heights of the other balls when any one reaches the jugglers hand.

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nautica

V(final) = V (original) + acceleration * time

or

Vf - Vo + at

You have only 3 points but 4 velocities, so I assume, your original or initial velocity would be u.

Have you tried this formula???

Nautica

Yes, ive used the formulae before, im having trouble with part two, the juggler question.

HallsofIvy
Homework Helper
Part two is relatively simple.

Each ball has acceleration -g= -9.81 m/s2. If we take "v" to be the initial velocity of each ball, then v(T)= v- 9.81T in m/s where T is measured in seconds since the ball was thrown.
In addition, the height of each ball after T seconds is given by
h(T)= vT- (9.81/2)T2.
The ball will continue upward until its velocity is 0: v- 9.81T= 0 so
T= v/9.81. We are told that the height at that time is 3 m:
v(v/9.81)- (9.81/2)(v/9.81)2= v2/(2*9.81)= 3 so