Question

1. a remote controlled car moves in a line. the graph below shows the distance,y, (in feet) a remote controlled car traveled away from the person controlling it, x seconds after turning it on.

which statement is true?
a. in section a, the remote control car increased its speed.
b. in section c the remote control car decreased its speed.
c. in section e, the remote control cars speed was 2 feet per 5 seconds.
d. in section g, the remote control cars speed was 3 feet per 5 seconds.

Explanation:

Step1: Analyze Section A

In a distance - time graph, speed is the slope of the line. For a straight - line section, the speed is constant. In Section A, it is a straight line, so the speed is constant, not increasing. So option a is wrong.

Step2: Analyze Section C

In Section C, it is a straight line. The slope of the line (which represents speed) is constant. So the speed is constant, not decreasing. So option b is wrong.

Step3: Analyze Section E

For Section E, we can use the slope formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let's take two points on Section E. Suppose \((x_1,y_1)=(60,9)\) and \((x_2,y_2)=(80,19)\). Then \(m=\frac{19 - 9}{80 - 60}=\frac{10}{20}=\frac{1}{2}\) feet per second. In terms of feet per 5 seconds, \(m=\frac{1}{2}\times5 = 2.5\) feet per 5 seconds. Another way: The change in \(y\) (distance) over a change in \(x\) (time). If we consider the time interval \(\Delta x = 10\) seconds (\(80 - 70\)) and \(\Delta y=10\) feet (\(19 - 9\)), the speed \(v=\frac{\Delta y}{\Delta x}\). For a 5 - second interval, if \(v = 1\) foot per second (since \(\frac{10}{10}=1\)), then in 5 seconds \(y = 5\) feet. Wait, let's use the formula correctly. The slope \(m=\frac{\Delta y}{\Delta x}\). For Section E, if we assume two points \((x_1,y_1)\) and \((x_2,y_2)\) such that \(x_2-x_1 = 10\) (say \(x_1 = 60,x_2=70\)) and \(y_2 - y_1=4\) ( \(y_1 = 9,y_2 = 13\)), \(m=\frac{4}{10}=\frac{2}{5}\) feet per second. In 5 seconds, the distance covered \(d=m\times5=\frac{2}{5}\times5 = 2\) feet.

Step4: Analyze Section G

For Section G, take two points \((x_1,y_1)=(80,20)\) and \((x_2,y_2)=(90,0)\). Then \(m=\frac{0 - 20}{90 - 80}=\frac{- 20}{10}=- 2\) feet per second. In terms of magnitude (speed), \(|m| = 2\) feet per second. In 5 seconds, the distance covered \(d = 2\times5=10\) feet. So the speed is \(2\) feet per second or \(10\) feet per 5 seconds, not \(3\) feet per 5 seconds.

Answer:

C. In Section E, the remote control car’s speed was 2 feet per 5 seconds.