A toy car accelerates from rest traveling in a straight line. Let \(d=s(t)\) represent the distance a toy car has moved away from its initial position (in feet) and let \(t\) represent the number of seconds elapsed since the toy car started moving. Values of \(d=s(t)\) for values of \(t = 1.5\) to \(t = 2\) are provided in the table below.
t d
1.5 22.5
1.6 25.6
1.7 28.9
1.8 32.4
1.9 36.1
2.0 40.0
Select each of the true statements from the following:
\(s(1.7)=28.9\)
The value \(t^*\) in the equation \(s(t^*)=28.9\) is the time (in minutes) it takes the car to travel \(28.9\) feet.
\(s(1.7)=1.7\)
The car travels \(1.7\) feet over the first \(28.9\) seconds of motion.
An approximation of the speed of the toy car \(1.7\) seconds after starting is \[ \frac{25.6 - 28.9}{0.1} \].
An overestimate of the speed of the toy car \(1.7\) seconds after starting is \[ \frac{28.9 - 25.6}{0.1} \].
An underestimate of the speed of the toy car \(1.7\) seconds after starting is \[ \frac{28.9 - 22.5}{0.2} \].
True. Looking at the table we can see that the value of \(d\) that corresponds to \(1.7\) is \(28.9\). Therefore, \(s(1.7)=28.9\).
False. The units of \(t\) are seconds, not minutes.
False. The \(s\) functions produces values of \(d\). The number \(1.7\) is not a value of \(d\).
False. Over the interval \([0,1.7]\) the car travels \(d=s(1.7) = 28.9\) feet.
False. The calculation \[ \frac{25.6 - 28.9}{0.1} \] is negative but the speed should be positive since the distances are increasing.
False. Since \(s\) is an increasing function and the car is accelerating, an overestimate of the speed of the toy car \(1.7\) seconds after starting is \[ \frac{32.4 - 28.9}{0.1} \]. An underestimate of this speed \[ \frac{28.9 - 25.6}{0.1} \]
False. Since \(s\) is an increasing function and the car is accelerating, an overestimate of the speed of the toy car \(1.7\) seconds after starting is \[ \frac{32.4 - 28.9}{0.1} \]. An underestimate of this speed \[ \frac{28.9 - 25.6}{0.1} \]
extype: mchoice exsolution: 1000000 exname: Approximating Instantaneous Rates of Change