A car travels on a straight road for 40km at 30km/h. It then continues in same direction for 40km at 60km/h.
a)What is the average velocity of the car during the 80km trip?(assume it moves in positive x direction)
b)What is the average speed?
c)graph and indicate how average velocity is fond on graph
a) I am confused when the car then changes its speed.
b)I forgot the equation for speed
c)Would I graph a position time graph and find out the area under the graph?
The confusion is this: Always, average speed is defined as
distance/time
distance= 40 km + 40 km
time= distance/vel= 40/30 + 40/60
avg speed= 80/(40/30 + 40/60)
in the case of going the same direction, avg speed = avg velocity
On the position time graph...
slope is veloicty. You know the veloicty for the first time of (40/30 hr), plot that line to that time. Then to the second line, starting at the end of the first.
You don't need area. For avg velocity, draw a line from the origin to the ned of the second line, and take the slope of that line....avg velocity= finalpositioin/time
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a) To find the average velocity of the car during the 80 km trip, we need to calculate the total displacement and divide it by the total time taken.
The car travels 40 km at a speed of 30 km/h, which takes:
time 1 = distance / speed = 40 km / 30 km/h = 4/3 hours.
The car then travels an additional 40 km at a speed of 60 km/h, which takes:
time 2 = distance / speed = 40 km / 60 km/h = 2/3 hours.
So, the total time taken for the 80 km trip is:
total time = time 1 + time 2 = 4/3 hours + 2/3 hours = 6/3 hours = 2 hours.
To calculate the total displacement, we must consider the direction. Since the car is moving in the positive x direction, the displacements in the opposite direction will have negative signs.
The first 40 km are in the positive direction, so the displacement is +40 km.
The second 40 km are also in the positive direction, so the displacement is +40 km.
Therefore, the total displacement is +40 km + 40 km = +80 km.
Average velocity = total displacement / total time
= 80 km / 2 hours = 40 km/h.
Therefore, the average velocity of the car during the 80 km trip is 40 km/h.
b) The equation for speed is the same as the equation for average velocity, which is distance divided by time:
speed = distance / time.
c) To graphically represent how average velocity is found on a graph, you can create a position-time graph.
On the position-time graph, plot the position of the car at different points in time. The slope of the line connecting two points on the graph represents the velocity at that particular time interval.
In this case, the car travels at a speed of 30 km/h for the first 40 km, so you can plot a line with a slope of 30 km/h. Then, from the end point of this line, plot another line with a slope of 60 km/h to represent the second part of the trip.
To find the average velocity, draw a line from the origin to the end point of the second line. The slope of this line represents the average velocity.
Please let me know if you need further clarification or assistance.
a) To find the average velocity of the car during the 80km trip, we need to calculate the total displacement and divide it by the total time taken.
Total displacement can be calculated by subtracting the initial position from the final position. In this case, the initial position is 0 km (assuming the car starts at the origin) and the final position is 80 km.
The total time taken can be calculated by adding the time taken for each segment of the trip. The first segment is 40 km at a speed of 30 km/h, so the time taken is 40 km / 30 km/h = 4/3 hours. The second segment is also 40 km but at a speed of 60 km/h, so the time taken is 40 km / 60 km/h = 2/3 hours.
The total time taken is (4/3 hours) + (2/3 hours) = 2 hours.
Therefore, the average velocity of the car during the 80km trip is (80 km - 0 km) / 2 hours = 40 km/h.
b) The equation for speed is distance divided by time. In this case, the total distance traveled is 80 km (40 km + 40 km) and the total time taken is 2 hours. So, the average speed is 80 km / 2 hours = 40 km/h.
c) To graphically find the average velocity on a position-time graph, you would plot the positions at different points in time and connect them with lines. The slope of each line represents the velocity at that specific time.
In this case, since the car is moving in the positive x direction, the initial position is at (0,0) and the final position is at (80,0) on the graph.
First, calculate the slope of the line for the first segment of the trip. The initial time is 0 hours and the final time is 4/3 hours. The position at the final time is (40,0), so the slope of this line represents the velocity during the first segment.
Next, calculate the slope of the line for the second segment of the trip. The initial time is 4/3 hours and the final time is 2 hours. The position at the final time is (80,0), so the slope of this line represents the velocity during the second segment.
Finally, draw a line from the origin (0,0) to the end point of the second line (80,0). The slope of this line represents the average velocity over the entire trip.