Question

Bryan is observing the velocity of a cyclist at different times. After four hours, the velocity of the cyclist is 15 km/h. After seven hours, the velocity of the cyclist is 12 km/h.
Part A: Write an equation in two variables in the standard form that can be used to describe the velocity of the cyclist at different times. Show your work and define the variables used. (5 points)

Part B: How can you graph the equations obtained in Part A for the first 12 hours? (5 points)

Answer 1

Part A.

What we can do to solve this problem is to assume that the acceleration of Bryan is constant so that the velocity function is linear. The standard form of a linear function is in the form:

y = m x + b

or in this case:

v = m t + b

where v is velocity and t is time, b is the y –intercept of the equation

The slope m can be calculated by:

m = (v2 – v1) / (t2 – t1)

m = (12 – 15) / (7 – 4)

m = -1

Since slope is negative therefore this means the cyclist are constantly decelerating. The equation then becomes:

v = - t + b

Now finding for b by plugging in any data pair:

15 = - (4) + b

b = 19

So the complete equation is:

v = - t + 19

This means that the initial velocity of the cyclists at t = 0 is 19 km / h.

 

Part B. What we can do to graph the equation is to calculate for the values of v from t = 0 to 12, then plot all these values in the Cartesian plane then connect the dots.