(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 a rock falls from rest from a height of 100 meters and the only force acting on it is gravity. Find an equation for the velocity v(t) as a function of time, measured in meters per second.
Hint
What is the initial velocity of the rock?
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
Chapter 5 Solutions
Calculus Early Transcendentals, Binder Ready Version
University Calculus: Early Transcendentals (4th Edition)
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