1) Two cars travel in the same direction along a straight road. The figure below shows the velocity, V, of each car at time t. Car B starts 3 hours after car A and car B reaches a maximum velocity of 40 km/hr.
a. For approximately how long does each car travel?
Car A: _______________ hours
Car B: _______________ hours
b. Estimate car A's maximum velocity. ____________ km/hr
c. Approximately how far does each car travel?
Car A: _________ km
Car B: _________ km
Ok I'm going to try and explain the graph. The y-axis is velocity in km/hr and the x-axis is time in hours. There are four marks on the x-axis ( not including (0,0) ) and two on the y-axis (not including (0,0) ). Car B has a triangle graph where the first point and the third point are at y=0 (I think the x-values might go up by three but I'm not sure because it doesn't have numbers) and the second point is the maximum peak which I think is 40. Car A also has a triangle graph but it is y=0 at x=0 and at the fourth point. It has its maximum peak on its second mark (x-axis) and second mark (y-axis which is think is 80 if the y's are going up by 40).
I know this is hard to do without being able to see the graph but please help me because I've tried seeing how to do this but I'm confused and have no idea where to start. Please show work. Thanks.
To solve this problem, we need to use the information given on the graph and apply some basic principles of motion.
a. For approximately how long does each car travel?
From the graph, we can see that Car B starts 3 hours after Car A. So, we can assume that the time for Car B is t - 3, where t is the time for Car A.
Using the graph for Car A, we see that it starts at (0,0), reaches a maximum at the second point, and returns to (0,0) at the fourth point. The duration for Car A can be calculated by finding the x-coordinate of the fourth point.
Similarly, for Car B, it starts at (3,0), reaches a maximum at the second point, and returns to (3,0) at the third point. The duration for Car B can be calculated by finding the x-coordinate of the third point.
b. Estimate car A's maximum velocity.
From the graph for Car A, we can see that the y-coordinate of the second point represents the maximum velocity. However, since there are no specific numbers on the y-axis, we will need to estimate the value.
c. Approximately how far does each car travel?
To find the distance traveled by each car, we need to calculate the area under each graph. Since the graph is triangular, we can use the formula for the area of a triangle: Area = (base * height) / 2.
Let's calculate the answers step by step:
a. For approximately how long does each car travel?
To find the duration for Car A, we need to determine the x-coordinate of the fourth point on its graph. Similarly, for Car B, we need to find the x-coordinate of the third point on its graph.
Without the specific values on the x-axis, it is difficult to accurately determine the time. However, you can estimate the values by dividing the total length (range) of the x-axis into four equal parts.
For example, if the x-axis represents a time range of 0-12 hours, you can estimate that the fourth point for Car A is located at approximately x = 9 hours, and the third point for Car B is located at approximately x = 6 hours.
b. Estimate car A's maximum velocity.
Since there are no specific values on the y-axis, we can estimate the values as well. Based on your description, you mentioned that the y-axis goes up by 40 units, and the maximum peak for Car A is at the second point.
If we assume that each unit on the y-axis represents 40 km/hr, we can estimate that the maximum velocity for Car A is approximately 80 km/hr.
c. Approximately how far does each car travel?
To calculate the distance traveled by each car, we need to find the area under the triangular graph.
For Car A, we can calculate the area of the triangle by using the formula: Area = (base * height) / 2. The base can be estimated as the time between the second and fourth points (approximately 6 hours), and the height is estimated as the maximum velocity (approximately 80 km/hr).
Distance traveled by Car A = Area = (6 * 80) / 2 = 240 km (approx.)
Similarly, for Car B, we can calculate the area of the triangle by using the formula: Area = (base * height) / 2. The base can be estimated as the time between the second and third points (approximately 3 hours), and the height is given as the maximum velocity, which is 40 km/hr.
Distance traveled by Car B = Area = (3 * 40) / 2 = 60 km (approx.)