A car travels in a straight line with an average velocity of 80 km/hr for 2.5 hours and then with an average velocity of 40 km/hr for 1.5 hours.
a. Calculate the largest displacement for the 4-hour trip.
b. Calculate the largest average velocity for the total trip in kilometers per hour.
Please if possible show all work, thanks for you help :)
80*2.5 + 40*1.5 = 200+60 = 260
What does it mean to say "largest average velocity for the total trip"?
There is only one average velocity for the total trip: 260/4 = 65 km/hr
I think they want you to say 80 km/hr, since after the first section the average velocity is lower. However, we know nothing about the velocity at other times. Maybe at some point in the first 2.5 hours the velocity was 300 km/hr, raising the average to 120 km/hr, but then slowed way down so at the end of the 2.5 hours, the average was only 80. Or, maybe at some point in the later section, again the velocity spiked way up, raising the average until then to some large amount.
If the question was posed as you typed it, it was very poorly worded.
a. To calculate the largest displacement for the 4-hour trip, we need to determine the total distance traveled during the different intervals.
For the first part of the trip, the car travels with an average velocity of 80 km/hr for 2.5 hours:
Distance1 = Velocity1 * Time1
Distance1 = 80 km/hr * 2.5 hr
Distance1 = 200 km
For the second part of the trip, the car travels with an average velocity of 40 km/hr for 1.5 hours:
Distance2 = Velocity2 * Time2
Distance2 = 40 km/hr * 1.5 hr
Distance2 = 60 km
To find the total displacement, we will add the individual distances:
Total Distance = Distance1 + Distance2
Total Distance = 200 km + 60 km
Total Distance = 260 km
Therefore, the largest displacement for the 4-hour trip is 260 km.
b. To calculate the largest average velocity for the total trip, we need to find the total displacement and divide it by the total time.
Total Time = Time1 + Time2
Total Time = 2.5 hr + 1.5 hr
Total Time = 4 hr
Therefore, the largest average velocity for the total trip is:
Average Velocity = Total Distance / Total Time
Average Velocity = 260 km / 4 hr
Average Velocity = 65 km/hr
So, the largest average velocity for the total trip is 65 km/hr.
To calculate the largest displacement for the 4-hour trip, we need to determine the total distance traveled during each leg of the journey.
For the first leg, the car travels at an average velocity of 80 km/hr for 2.5 hours. To find the distance traveled, we can use the formula:
Distance = Velocity x Time
Distance = 80 km/hr x 2.5 hr = 200 km
For the second leg, the car travels at an average velocity of 40 km/hr for 1.5 hours. Using the same formula:
Distance = 40 km/hr x 1.5 hr = 60 km
To find the largest displacement, we need to consider the direction traveled during each leg. Since the car travels in a straight line, we can subtract the distance of the second leg from the distance of the first leg to determine the largest displacement:
Largest Displacement = 200 km - 60 km = 140 km
Therefore, the largest displacement for the 4-hour trip is 140 km.
To calculate the largest average velocity for the total trip, we need to consider the total distance traveled during the 4-hour trip and the total time taken.
Total Distance = Distance of the first leg + Distance of the second leg = 200 km + 60 km = 260 km
Total Time = Time of the first leg + Time of the second leg = 2.5 hr + 1.5 hr = 4 hr
To find the largest average velocity, we can use the formula:
Average Velocity = Total Distance / Total Time
Average Velocity = 260 km / 4 hr = 65 km/hr
Therefore, the largest average velocity for the total trip is 65 km/hr.