You dive a car 2.0 h at 40km/h , then 2.0 h at 60 km/h
A) what is you average velocity
B) do you get the same answer if you drive 100 km at each of the two speeds above
A. d = 40*2 + 60*2 = 200 km.
Vavg = 200/4 = 50 km/h.
B. d1 = 40*T1 = 100.
T1 = 2.5 h.
d2 = 60*T2 = 100.
T2 = 1.7 h,
Vavg. = (d1+d2)/(T1+T2) = 200/4.2 = 47.6 km/h.
To find the average velocity, we need to calculate the total displacement and divide it by the total time.
A) To calculate the total displacement, we can add the individual displacements during each interval of time. The displacement for the first interval can be found using the formula: displacement = velocity × time. The displacement for the second interval can also be found using the same formula.
For the first interval: Displacement1 = velocity1 × time1 = 40 km/h × 2.0 h
For the second interval: Displacement2 = velocity2 × time2 = 60 km/h × 2.0 h
Add the two displacements together to get the total displacement:
Total Displacement = Displacement1 + Displacement2
Now, to calculate the average velocity:
Average Velocity = Total Displacement / Total Time
B) If you drive 100 km at each of the two speeds, the approach to calculating the average velocity remains the same.
For the first interval of 100 km distance at 40 km/h:
Displacement1 = velocity1 × time1 = 40 km/h × (100 km / 40 km/h)
For the second interval of 100 km distance at 60 km/h:
Displacement2 = velocity2 × time2 = 60 km/h × (100 km / 60 km/h)
Again, add the two displacements together to get the total displacement:
Total Displacement = Displacement1 + Displacement2
Calculate the average velocity using the formula:
Average Velocity = Total Displacement / Total Time
So, whether you drive for 2.0 hours or 100 km at each of the two speeds, the average velocity will be the same as long as the total displacement and total time are the same.