Question

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.

Answer #1

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 with constant acceleration is
given by
x(t) = 4t2 + 3t +
4
where x is in meters and t is in seconds.
(a) Calculate the average velocity of this particle between
t = 2 seconds and t = 7 seconds.
(b) At what time during this interval is the average velocity equal
to the instantaneous velocity?
(c) How does this time compare to the average time for this
interval?
a. It is larger....

The position of a particle moving with constant acceleration is
given by x(t) = 2t2 +
8t + 4 where x is in meters and t is in
seconds.
(a) Calculate the average velocity of this particle between
t = 6 seconds and t = 9 seconds.
(b) At what time during this interval is the average
velocity equal to the instantaneous velocity?

please do 1,2 and 3 thanks
1.The position of a particle moving along the x axis is
given in centimeters by x = 9.12 + 1.75
t3, where t is in seconds. Calculate
(a) the average velocity during the time interval
t = 2.00 s to t = 3.00 s; (b)
the instantaneous velocity at t = 2.00 s;
(c) the instantaneous velocity at t =
3.00 s; (d) the instantaneous velocity at
t = 2.50 s; and (e) the...

The position ? of a particle moving in space from (t=0 to 3.00
s) is given by ? = (6.00?^2− 2.00t^3 )i+ (3.00? − ?^2 )j+ (7.00?)?
in meters and t in seconds. Calculate (for t = 1.57 s): a. The
magnitude and direction of the velocity (relative to +x). b. The
magnitude and direction of the acceleration (relative to +y). c.
The angle between the velocity and the acceleration vector. d. The
average velocity from (t=0 to 3.00 s)....

The position of a particle moving along the x axis is
given in centimeters by x = 9.31 + 1.02
t3, where t is in seconds. Calculate
(a) the average velocity during the time interval
t = 2.00 s to t = 3.00 s; (b)
the instantaneous velocity at t = 2.00 s;
(c) the instantaneous velocity at t =
3.00 s; (d) the instantaneous velocity at
t = 2.50 s; and (e) the instantaneous
velocity when the particle is...

The position of a particle moving along the x axis is
given in centimeters by x = 9.58 + 1.68
t3, where t is in seconds. Calculate
(a) the average velocity during the time interval
t = 2.00 s to t = 3.00 s; (b)
the instantaneous velocity at t = 2.00 s;
(c) the instantaneous velocity at t =
3.00 s; (d) the instantaneous velocity at
t = 2.50 s; and (e) the instantaneous
velocity when the particle is...

The position of a particle moving along the x axis is given in
centimeters by x = 9.16 + 1.52 t3, where t is in seconds. Calculate
(a) the average velocity during the time interval t = 2.00 s to t =
3.00 s; (b) the instantaneous velocity at t = 2.00 s; (c) the
instantaneous velocity at t = 3.00 s; (d) the instantaneous
velocity at t = 2.50 s; and (e) the instantaneous velocity when the
particle is...

The position of a particle moving along the x axis is
given in centimeters by x = 9.18 + 1.66
t3, where t is in seconds. Calculate
(a) the average velocity during the time interval
t = 2.00 s to t = 3.00 s; (b)
the instantaneous velocity at t = 2.00 s;
(c) the instantaneous velocity at t =
3.00 s; (d) the instantaneous velocity at
t = 2.50 s; and (e) the instantaneous
velocity when the particle is...

The position of a particle moving along the x axis is
given in centimeters by x = 9.75 + 2.50t
3, where t is in seconds. Consider the time
interval t = 2.00 s to t = 3.00 s.
(a) Calculate the average velocity.
(b) Calculate the instantaneous velocity at t = 2.00
s.
(c) Calculate the instantaneous velocity at t = 3.00
s.
(d) Calculate the instantaneous velocity at t = 2.50
s.
(e) Calculate the instantaneous velocity when...

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