A particle moves with position r(t) =
x(t) i + y(t)
j where x(t) =
10t2 and y(t) = -3t
+ 2, with x and y in meters and t in seconds.
(a) Find the average velocity for the time interval from 1.00 s
to 3.00 s.
(b) Find the instantaneous velocity at t = 1.00 s.
(c) Find the average acceleration from 1.00 s to 3.00 s.
(d) Find the instantaneous acceleration at t = 1.00 s.
A particle of mass 2.00 kg moves with position r(t) = x(t)
i + y(t) j where x(t) =
10t2 and y(t) = -3t + 2, with x and y in meters and t in
seconds.
(a) Find the momentum of the particle at time t = 1.00 s.
(b) Find the angular momentum about the origin at time t = 3.00
s.
A particle of mass 2.00 kg moves with position r(t) = x(t) i +
y(t) j where x(t) = 10t2 and y(t) = -3t + 2, with x and y in meters
and t in seconds.
(a) Find the momentum of the particle at time t = 1.00
s.
(b) Find the angular momentum about the origin at time t =
3.00 s.
The position of a particle moving along the x-axis is given by
x(t) = t^3 + 9t^2 − 21t with t is in [0, 2]. (a) Find the velocity
and acceleration of the particle.
(b) For what t-values is the velocity 0? (Enter your answers as
a comma-separated list.)
(c) When is the particle moving to the left (velocity is
negative)? (Enter your answer using interval notation.)
When is the particle moving to the right (velocity is positive)?
(Enter your...
The position x of an object varies with time
t. For which of the following equations relating
x and t is the motion of the object simple
harmonic motion? (There may be more than one correct choice.)
The position x of an object varies with time
t. For which of the following equations relating
x and t is the motion of the object simple
harmonic motion? (There may be more than one correct choice.)
x = 5 sin23t
x =...
Find the distance between the skew lines with parametric
equations x = 1 + t, y = 3 +
6t, z = 2t, and
x = 1 + 2s, y = 6 + 15s, z
= −2 + 6s.
Find the equation of the line that passes through the points on
the two lines where the shortest distance is measured.
The position of a particle is given by x = 1/3t3 - 2t2 and y =
1/2t2 - 2t. Positions are in meters and time is in seconds.
Complete the following table. θ is the angle between v and a, dv/dt
is the rate at which the speed is changing, and R is the radius of
the trajectory's tangent circle.
t (s)
v (m/s)
a (m/s/s)
θ (deg)
dv/dt (m/s/s)
R(m)
2.00
i + j
i + j
3.00
i...