(a) Suppose that the acceleration function of a particle moving along a coordinate line is a t = t + 1 . Find the average acceleration of the particle over the time interval 0 ≤ t ≤ 5 by integrating. (b) Suppose that the velocity function of a particle moving along a coordinate line is υ t = cos t . Find the average acceleration of the particle over the time interval 0 ≤ t ≤ π / 4 algebraically.
(a) Suppose that the acceleration function of a particle moving along a coordinate line is a t = t + 1 . Find the average acceleration of the particle over the time interval 0 ≤ t ≤ 5 by integrating. (b) Suppose that the velocity function of a particle moving along a coordinate line is υ t = cos t . Find the average acceleration of the particle over the time interval 0 ≤ t ≤ π / 4 algebraically.
(a) Suppose that the acceleration function of a particle moving along a coordinate line is
a
t
=
t
+
1
. Find the average acceleration of the particle over the time interval
0
≤
t
≤
5
by integrating.
(b) Suppose that the velocity function of a particle moving along a coordinate line is
υ
t
=
cos
t
. Find the average acceleration of the particle over the time interval
0
≤
t
≤
π
/
4
algebraically.
With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.
1.) Let s(t)= tlnt-t be the displacement of a particle (in feet) from the origin after t seconds.
a.) Find the velocity of the particle at 5 seconds. (Show all your work and include units)
b.) Find the acceleration of the particle after 5 seconds. (Show all your work and include units)
The acceleration function (in m/s?) and the initial velocity v(0) are given for a particle moving along a line.
a(t) = 2t + 2, v(0) = -15, 0sts 5
(a) Find the velocity at time t.
v(t) =
m/s
(b) Find the distance traveled during the given time interval.
(1) A particle has an initial displacement of s = 30 metres when t = 0. The velocity
of the particle is v= 6t² - 216t+ 1944 m/s (t > 0).
(a) Find the displacement of the particle at time t.
(b) Find the acceleration of the particle at time t.
(c) What is the acceleration and displacement when v = 0?
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