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
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
Related Flashcard Decks
| Term | Definition |
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More on Instantaneous Rate |
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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 |