(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.
Suppose an object is moving along a line such that the acceleration after t seconds is
6t -8t (ft/sec)/sec. If its velocity after 1 second is 2 ft/sec and its initial position is 3
ft, find its position after 4 seconds.
A raindrop falls with acceleration 9.8
m/sec² , where "v" is its velocity. What is the
raindrop's velocity?
29.4(1 – e3) m/sec
29.4(e- 1) m/sec
29.4(1 – e5) m/sec
32.2 (e- 1) m/sec
The velocity of a material point that starts moving on a linear trajectory from the point
X = 0 is V= 50 -x, (m/ sn). Calculate its acceleration at x= 60 m. Obtain the location of this
material point as a function of time.
Chapter 5 Solutions
Calculus Early Transcendentals, Binder Ready Version
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