Question 1208332
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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.<br>
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.<br>
So the linear function can now be written as y=-5x+b.<br>
Use either of the two given data points to determine the value of b.  The speed is 60 at t=1:<br>
60 = -5(1)+b
60 = -5+b
b = 65<br>
And now we have the full linear equation: y = -5x+65<br>
Or, in formal function notation showing speed as a function of time...<br>
ANSWER: s(t)=-5t+65<br>
To find when the car's speed is 0, set s(t)=0 and solve.<br>
-5t+65 = 0
5t = 65
t = 13<br>
ANSWER: at 13 seconds<br>