Question

Three cars start at the same time and travel at different constant rates. The motion is represented in the graph for car A and car B. The equation of motion of the car A: $0.5y=25x$. Throughout the journey, car C remains equidistant from car B and car A. What will be the distance traveled by car C when car A has traveled $300$ miles?
[Hint: Average speed = Slope of the distance-time graph $=\frac{\text{Distance traveled}}{\text{Time taken}}$]

Answer 1

Detailed step-by-step solution:
Finding the average speed of car A:
$0.5y=25x$
$\Rightarrow y=\frac{25}{0.5}x$
$\Rightarrow y=50x$
Average speed of car A $=\frac{\text{Distance traveled}}{\text{Time taken}}$
$=\frac{y}{x}$
$=\frac{50x}{x}$
$=50$ miles/hr
Calculating the time taken by car A when it has traveled $300$ miles:
Average speed of car A $=\frac{\text{Distnace traveled}}{\text{Average speed}}$
$=\frac{300miles}{50miles/hr}$
$=6hr$

Finding the average speed of car B:
Finding the slope of the graph:
Let’s consider two points $(0,0)$ and $(4,240)$ on the graph:
$\text{Slope}=\frac{\text{Rise}}{\text{Run}}$
$=\frac{\text{Change in y}}{\text{Change in x}}$
$=\frac{240-0}{4-0}$
$=\frac{240}{4}$
$=60$
Average speed of car B = Slope of the distance-time graph
$=60$ miles/hr
Calculating the distance traveled by car B when car A has traveled $300$ miles:

Average speed of car B $=\frac{\text{Distance traveled}}{\text{Time taken by Car A in traveling 300 miles}}$
$=60$ miles/hr $=\frac{\text{Distance traveled}}{6hr}$
$\Rightarrow$Distance traveled $=60\times 6$ miles
$=360$ miles
Let distance traveled by car C when car A has traveled $300$ miles and at the same time Car B has traveled $360$ miles be d.
Distance between cars B and C = Distance between cars C and A (Car C always remains equidistant from
car B and car A)
$\Rightarrow 360-d=d-300$
$\Rightarrow 2d=360+300$
$\Rightarrow 2d=660$
$\Rightarrow \frac{660}{2}$
$\Rightarrow d=330$ miles
The distance traveled by car C is 330 miles.
Option C is correct.