You drive a car for 2.0 h at 35 km/h, then for another 2.0 h at 64 km/h.
(a) What is your average velocity?
(b) What is your answer if instead you drive 99 km at each of the two speeds?
To find the average velocity, we need to calculate the total displacement and divide it by the total time taken.
(a) For the first scenario, you drove for 2.0 hours at 35 km/h and then for another 2.0 hours at 64 km/h.
To find the total displacement, we need to calculate the distance traveled at each speed and then add them together.
Distance at 35 km/h:
Distance = Speed × Time
Distance = 35 km/h × 2.0 h
Distance = 70 km
Distance at 64 km/h:
Distance = Speed × Time
Distance = 64 km/h × 2.0 h
Distance = 128 km
The total displacement is the sum of the distances:
Total Displacement = 70 km + 128 km
Total Displacement = 198 km
Now, we can calculate the average velocity:
Average Velocity = Total Displacement / Total Time
Average Velocity = 198 km / 4.0 h
Average Velocity = 49.5 km/h
Therefore, the average velocity for this scenario is 49.5 km/h.
(b) For the second scenario, you drove 99 km at each of the two speeds.
Again, we need to calculate the total displacement and divide it by the total time taken.
Distance at 35 km/h:
Distance = Speed × Time
Distance = 35 km/h × (99 km / 35 km/h)
Distance = 99 km
Distance at 64 km/h:
Distance = Speed × Time
Distance = 64 km/h × (99 km / 64 km/h)
Distance = 99 km
The total displacement is the sum of the distances:
Total Displacement = 99 km + 99 km
Total Displacement = 198 km
The total time taken is the sum of the times at each speed:
Total Time = 99 km / 35 km/h + 99 km / 64 km/h
Total Time = 2.83 h + 1.54 h
Total Time = 4.37 h
Now, we can calculate the average velocity:
Average Velocity = Total Displacement / Total Time
Average Velocity = 198 km / 4.37 h
Average Velocity ≈ 45.32 km/h
Therefore, the average velocity for the second scenario is approximately 45.32 km/h.