Sam is observing the velocity of a car at different times. After three hours, the velocity of the car is 53 km/h. After six hours, the velocity of the car is 62 km/h.
Part A: Write an equation in two variables in the standard form that can be used to describe the velocity of the car at different times. Show your work and define the variables used. (5 points)
Part B: How can you graph the equation obtained in Part A for the first seven hours?
The assumption we have to make is that the velocity is a linear function of the time ....
So we have two ordered pairs (3,53) and (6,62)
slope = (62-53)/(6-3)
= 3
using the point (3,53)
v-53 = 3(t-3)
v-53 = 3t - 9
3t - v = - 44 or y = 3t + 44
should be easy to plot for 3 < t < 7
thnx
can you help me with one more?
Part A:
Let's define the variables used in the equation:
- "t" represents time in hours
- "v" represents the velocity of the car in km/h
To create the equation, we need to find the relationship between time and velocity. We can assume that the velocity is changing linearly over time.
We are given two points: (3, 53) and (6, 62). This means that after 3 hours, the velocity is 53 km/h, and after 6 hours, the velocity is 62 km/h.
Using the formula for the slope of a line:
slope (m) = (change in y) / (change in x)
Let's calculate the slope:
slope = (62 - 53) / (6 - 3)
= 9 / 3
= 3
Now we have the slope, and we can use the point-slope form of a linear equation:
v - v₁ = m(t - t₁)
Using the point (3, 53):
v - 53 = 3(t - 3)
Expanding the equation:
v - 53 = 3t - 9
Rearranging the equation to the standard form:
3t - v = -9 + 53
3t - v = 44
So, the equation in two variables in the standard form that can be used to describe the velocity of the car at different times is 3t - v = 44.
Part B:
To graph the equation 3t - v = 44 for the first seven hours, we need to plot points on a coordinate plane.
We can choose any values for "t" between 0 and 7 and substitute them into the equation to find the corresponding values for "v."
For example, let's choose t = 0:
3(0) - v = 44
0 - v = 44
-v = 44
v = -44
So, when t = 0, v = -44. This gives us the point (0, -44) on the graph.
Similarly, we can choose other values for "t" within the range. For instance, when t = 1, we have:
3(1) - v = 44
3 - v = 44
-v = 44 - 3
-v = 41
v = -41
Thus, when t = 1, v = -41. This gives us the point (1, -41) on the graph.
By repeating this process for other values of "t," we can generate more points on the graph. Once we have enough points, we can plot them on the coordinate plane and connect them with a straight line.