Recall that if s(t) represents the position at time t of any object moving in a straight line, then its velocity is given by the derivative  v(t) = s'(t). Now, suppose that object is a car. Since a car rarely drives at a constant speed, the velocity itself may be changing. The rate at which the velocity is changing is the acceleration. Because the derivative measures the rate of change, acceleration is the derivative of velocity  a(t) = v'(t). So, to determine acceleration, first find velocity. Given that  s(t) = 130 + 13t − 0.8t2,  the velocity  v(t)  is found by taking the  ---Select--- first second third derivative of position,  s'(t). Since  s'(t) = 13 −       t,  we have  v(t) =

Calculus: Early Transcendentals
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ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
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Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Recall that if s(t) represents the position at time t of any object moving in a straight line, then its velocity is given by the derivative 
v(t) = s'(t).
Now, suppose that object is a car. Since a car rarely drives at a constant speed, the velocity itself may be changing. The rate at which the velocity is changing is the acceleration. Because the derivative measures the rate of change, acceleration is the derivative of velocity 
a(t) = v'(t).
So, to determine acceleration, first find velocity.
Given that 
s(t) = 130 + 13t − 0.8t2,
 the velocity 
v(t)
 is found by taking the  ---Select--- first second third derivative of position, 
s'(t).
Since 
s'(t) = 13 − 
 
  
 
t,
 we have 
v(t) = 
 
 
 
 .
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