PROBLEMS
1.1 The motion of a particle is defined by the relation x = t4 – 10t2 + 8t + 12,
where x and t are expressed in meters and seconds, respectively.
Determine the position, the velocity, and the acceleration of the particle
when t = 1 s.
1.2 The motion of a particle is defined by the relation x = 2t3 – 9t2 + 12t +
10, where x and t are expressed in meters and seconds, respectively.
Determine the time, the position, and the acceleration of the particle when
v = 0.
1.3 The motion of a particle is defined by the relation x = 6t4 – 2t3 – 12t2 +
3t + 3, where x and t are expressed in meters and seconds, respectively.
Determine the time, the position, and the velocity when a = 0.
1.4 The motion of a particle is defined by the relation x = t3 – 9t2 + 24t – 8,
where x and t are expressed in inches and seconds, respectively. Determine
(a) when the velocity is zero, (b) the position and the total distance traveled
when the acceleration is zero.
1.5 The motion of a particle is defined by the relation x = 2t3 – 15t2 + 24t +
4, where x is expressed in meters and t in seconds. Determine (a) when the
velocity is zero, (b) the position and the total distance traveled when the
acceleration is zero.
1.6 The motion of a particle is defined by the relation x = t3 – 6t2 – 36t – 40,
where x and t are expressed in meters and seconds, respectively.
Determine (a) when the velocity is zero, (b) the velocity, the acceleration,
and the total distance traveled when x = 0.
1.7 Starting from the origin, the velocity of a particle which moves along
the x-axis is given by v = 40 – 3t2 m/s where t is in seconds. Calculate the
net displacement Δx of the particle during the interval from t = 2 s to t = 4 s.
1.8 Starting from the origin, a particle moves along a straight line with a
velocity in millimeters per second given by v = 400 – 16t2, where t is in
seconds. Calculate the net displacement Δx and total distance D traveled
during the first 6 seconds of motion.
1.9 Starting from rest at the origin, the acceleration of a particle is given by
a = 4t – 30, where a is in meters per second squared and t is in seconds.
Determine the velocity and displacement as functions of time.
1.10 The velocity of a particle is given by v = 2 + 5 t3/2, where t is in seconds
and v is in meters per second. Evaluate the displacement x, velocity v, and
acceleration a when t = 4 s. The particle is at the origin x = 0 when t = 0.
1.11 The position of a particle which moves along a straight line is defined
by the relation x = t3 – 27t + 15, where x is expressed in meters and t in
seconds. Determine:
(a) the time t at which the velocity v will be zero,
(b) the acceleration of the particle when v = 48 m/s,
(c) the total distance D traveled of the particle during the interval from
t = 2 s to t = 5 s.
1.12 Starting from rest at the origin, a particle moving in a straight line has
an acceleration of a = 2t – 9, where a is in m/s2 and t in seconds. Determine:
(a) the velocity v at t = 9 s,
(b) the velocity v at a = 11 m/s2,
(c) the total distance D traveled during the interval from t = 6 s to
t = 12 s.
1.13 A particle moves along a straight line with a velocity in meters per
second given by v = 3t2 – 6t, where t is in seconds. The particle is at the
origin x = 0 when t = 0. Determine:
(a) the acceleration a at t = 4 s,
(b) the velocity v at t = 2 s,
(c) the net displacement Δx and the total distance D traveled during the
interval from t = 1 s to t = 6 s.