AP Calculus AB: 3.2.4 More on Instantaneous Rate
To find when an object reaches a specific location, set the position function equal to that location and solve for time. The instantaneous velocity is found by taking the derivative and evaluating it at a given time. An object stops when its velocity (derivative) equals zero.
More on Instantaneous Rate
Set the position function equal to a specific location to find the time that an object reaches that point. Substitute the specified time into the derivative of the position function to find the velocity of an object at that time.
Set the derivative of the position function equal to zero to find when the object stops.
Key Terms
More on Instantaneous Rate
Set the position function equal to a specific location to find the time that an object reaches that point. Substitute the specified time in...
note
Suppose you are given the position function for a particular object.
To find the time that an object reaches a particular lo...
The rate of production at ACME toys can be determined from the production formula P(t)=1600t−100t^2, where P(t)is the number of units produced in a given time and t is the time in hours since the factory shift began. At what time does the rate of toy production equal 1300 units per hour?
1.5 hours
A particle moves along a straight line with its position given by the function p=f(t)=3t^2−2t+4, where p is given in meters and t in seconds. For what value of t does the velocity of the particle equal10 meters per second?
t = 2
A particle moves along a straight line with its position given by the function p=f(t)=t^2−5t+4, where p is given in meters and t in seconds. When does the velocity equal 24 meters per second?
t = 14.5
The rate of production at ACME toys can be determined from the production formula P(t) = 1600t − 100t^2, where P(t) is the number of units produced in a given time and t is the time in hours since the factory shift began. At what time does toy production stop?
8 hours
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| Term | Definition |
|---|---|
More on Instantaneous Rate |
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note |
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The rate of production at ACME toys can be determined from the production formula P(t)=1600t−100t^2, where P(t)is the number of units produced in a given time and t is the time in hours since the factory shift began. At what time does the rate of toy production equal 1300 units per hour? | 1.5 hours |
A particle moves along a straight line with its position given by the function p=f(t)=3t^2−2t+4, where p is given in meters and t in seconds. For what value of t does the velocity of the particle equal10 meters per second? | t = 2 |
A particle moves along a straight line with its position given by the function p=f(t)=t^2−5t+4, where p is given in meters and t in seconds. When does the velocity equal 24 meters per second? | t = 14.5 |
The rate of production at ACME toys can be determined from the production formula P(t) = 1600t − 100t^2, where P(t) is the number of units produced in a given time and t is the time in hours since the factory shift began. At what time does toy production stop? | 8 hours |
The rate of production at ACME toys can be determined from the production formula P(t)=1600t−100t^2, where P(t)is the number of units produced in a given time and t is the time in hours since the factory shift began. A factory shift lasts8 hours. After what amount of time does the number of toys produced equal4800? | 4 hours |
A particle moves along a straight line with | t = 1 |