(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.
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