Question

Brandon went to a Formula One car race and used his stopwatch to time how fast his favorite driver, Fernando Alonso, went around the 4.7-kilometer track. Brandon started the timer at the beginning of the second lap when the cars were already going fast. When he stopped the timer at the beginning of the third lap, one minute and three seconds had passed.

a. What was the average speed of Fernando Alonso, in kilometers per hour? What does it mean for this speed to be the “average”?

b. If you graphed the distance Fernando had traveled at the beginning of the lap and at the end of the lap, what would the coordinates of these points be? What would the - and -axes on this graph represent?

c. Find the equation of the line between these two points. What does this line represent? d. If Fernando continues to average this speed, about how long do you think it would take him to finish the entire race? The race is 500 km.

Answer 1

(A)

To calculate the speed you use the formula V=distance/time. We also need to convert the time into hours so V would be

V=(4.7x3600)/63=268.57km/h.

Average speed is the average of top speed and lowest speed and it need not necessarily be the constant speed throughout.  

(B) If we had to plot a graph to represent the coordinates at the starting of a lap and coordinates at the end of the lap. We will use time t in seconds on x-axis and distance d in metres on y-axis. Let's assume coordinates at the starting of a lap are as origin or (0,0). Therefore coordinates at the end of a lap will be (63,4700) since in 63 seconds fernando has crossed 4.7km=4700m. X-axis of this graph represents time and Y-axis represents distance.

(C) for, equation of line we need slope and one point.

slope=4700-0/63-0

=4700/63

=78.33

as line passes through (0,0), Equation of line:

y-0=78.33(x-0)

y=78.33x

This line represents distance travelled by Fernando in any given amount of time. Slope of this line represents Speed.

(D)time taken to cover D=500km will be:

t=distance/speed

=500/268.57

= 1.86 hours or 1 hour and 51.6 minutes.