SOLUTION: The car's speed decreased linearly as a function of time. The speed was 60 kph at t=1s and 40 kph at t = 5 s. Create a function that describes speed as a function of time. At what

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Question 1208332: The car's speed decreased linearly as a function of time. The speed was 60 kph at t=1s and 40 kph at t = 5 s. Create a function that describes speed as a function of time. At what time did the car's speed equal 0?
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52803)   (Show Source): You can put this solution on YOUR website!
.
The car's speed decreased linearly as a function of time.
The speed was 60 kph at t=1s and 40 kph at t = 5 s.
Create a function that describes speed as a function of time. At what time did the car's speed equal 0?
~~~~~~~~~~~~~~~~~~~~~~~~

The function is  

    f(t) = V - at,    (1)


where V is the initial speed at t= 0, "a" is the rate of the speed decreasing, t is the time (in seconds).


We don't know V at t= 0  (it is not given),  but we can easily find "a".



"a" is the ratio of the change of the speed to the elapsed time

    a =  =  = 5 kilometer per hour per second.



Now from equation (1) we will find V

    V - 5*1 = 60 ,

    V = 60 + 5 = 65.


Thus the function is  f(t) = 65 - 5t kilometers per hour.    ANSWER



To find the stop time, write this equation

    V = 65 - 5t = 0.


From the equation,  t = 65/5 = 13 seconds from the beginning.    ANSWER

Solved, with all necessary explanations.



Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


We are told that the speed as a function of time is linear, so let's use the standard notation for a linear function: y = mx+b where the dependent variable y is the car's speed and the independent variable x is the time in seconds.

In the standard form y=mx+b, m is the slope, or rate of change. In this problem, the speed decreased from 60kph to 40kph, a change of -20kph, in 4 seconds, between t=1 and t=5. So the slope m is -20/4 = -5.

So the linear function can now be written as y=-5x+b.

Use either of the two given data points to determine the value of b. The speed is 60 at t=1:

60 = -5(1)+b
60 = -5+b
b = 65

And now we have the full linear equation: y = -5x+65

Or, in formal function notation showing speed as a function of time...

ANSWER: s(t)=-5t+65

To find when the car's speed is 0, set s(t)=0 and solve.

-5t+65 = 0
5t = 65
t = 13

ANSWER: at 13 seconds


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