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PROBLEM 11.19
Based on experimental observations, the acceleration of a particle is defined by the relation (0.1a sin x/b),
where a and x are expressed in m/s2 and meters, respectively. Knowing that 0.8 mb and that 1 m/sv
when 0,x determine (a) the velocity of the particle when 1 m,x
(b) the position where the velocity is
maximum, (c) the maximum velocity.
PROBLEM 11.20
A spring AB is attached to a support at A and to a collar. The
unstretched length of the spring is l. Knowing that the collar is
released from rest at 0
x
x
and has an acceleration defined by
the relation 22
100( / ) axlxlx
, determine the velocity of
the collar as it passes through Point C.
PROBLEM 11.21
The acceleration of a particle is defined by the relation
1,
x
ak e
where k is a constant. Knowing that
the velocity of the particle is 9v m/s when 3x
m and that the particle comes to rest at the origin,
determine (a) the value of k, (b) the velocity of the particle when 2x
m.
PROBLEM 11.22
Starting from
x
0 with no initial velocity, a particle is given an acceleration
2
0.1 16,av
where
a
and
v
are expressed in ft/s
2
and ft/s, respectively. Determine (
a
) the position of the particle when
v
3ft/s, (
b
) the speed and acceleration of the particle when
x
4 ft.
PROBLEM 11.23
A ball is dropped from a boat so that it strikes the surface of a
lake with a speed of 16.5 ft/s. While in the water the ball
experiences an acceleration of 10 0.8 ,av
where
a
and
v
are expressed in ft/s
2
and ft/s, respectively
. Knowing the
ball takes 3 s to reach the bottom of the lake, determine (a) the
depth of the lake, (b) the speed of the ball when it hits the
bottom of the lake.
PROBLEM 11.23 (Continued)
t
PROBLEM 11.24
The acceleration of a particle is defined by the relation ,akv where k is a constant. Knowing that x 0
and v 81 m/s at t 0 and that v 36 m/s when x 18 m, determine (a) the velocity of the particle when
x 20 m, (b) the time required for the particle to come to rest.
PROBLEM 11.25
The acceleration of a particle is defined by the relation 2.5,akv where k is a constant. The particle starts at
0x with a velocity of 16 mm/s, and when 6x
mm the velocity is observed to be 4 mm/s. Determine
(a) the velocity of the particle when 5x mm, (b) the time at which the velocity of the particle is 9 mm/s.
PROBLEM 11.25 (Continued)
Problem 11.26
A human powered vehicle (HPV) team wants to model the
acceleration during the 260 m sprint race (the first 60 m is called a
flying start) using a = A – Cv
2
, where a is acceleration in m/s
2
and v
is the velocity in m/s. From wind tunnel testing, they found that
C = 0.0012 m
-1
. Knowing that the cyclist is going 100 km/h at the
260 meter mark, what is the value of A?
