A car travels a straight road at 140 km/h for 30 min then at 90 km/h for 10 min. It then reverses and goes at 90 km/h for 20 min.
a) Find the average velocity for the entire trip.
b) Find the average speed for the entire trip.
30 min = .5 h
10 min = 1/6 h
20 min = 1/3 h
=================
d = 140*.5 + 90/6 + 90/3
(it went 90 for a total of 1/2hour???? typo I bet)
average speed = d /total time
the way you wrote it the total time is one hour, but I doubt it.
The three legs of the trip are
70 km , 15 km , and 30 km for a total time of 1 hour
average velocity = (70 + 15 - 30)/1 = 55 km/h
average speed = (70+15+30)/1 = 115 km/h
velocity involves both magnitude and direction.
Since the direction was reversed for the last part, I used -30
I did not see the reversal of direction
To find the average velocity and average speed for the entire trip, we first need to understand the definitions of velocity and speed.
Velocity is a vector quantity that is defined as the rate of change of displacement. It takes into account both the magnitude and direction of motion, and is measured in units of distance per unit time (e.g., meters per second, kilometers per hour).
Speed, on the other hand, is a scalar quantity that represents the rate of change of position. It only considers the magnitude of motion, without any regard for direction, and is measured in units of distance per unit time.
Now let's calculate the average velocity and average speed for the given situation:
a) Average velocity for the entire trip:
To find the average velocity, we need to divide the total displacement by the total time taken.
1. Calculate the total distance traveled during each segment of the trip:
- In the first segment, the car travels at 140 km/h for 30 minutes. As distance = speed × time, the distance traveled in this segment is 140 km/h × (30 min / 60 min/h) = 70 km.
- In the second segment, the car travels at 90 km/h for 10 minutes. Again, using the same formula, the distance traveled in this segment is 90 km/h × (10 min / 60 min/h) = 15 km.
- In the final segment, the car reverses and goes at 90 km/h for 20 minutes. Applying the formula, the distance traveled in this segment is 90 km/h × (20 min / 60 min/h) = 30 km.
2. Calculate the total displacement. Since the car returns to its starting point, the displacement is zero (since it's a round trip).
3. Now, we can calculate the total time taken. Adding the times for each segment, the total time taken is 30 min + 10 min + 20 min = 60 min (1 hour).
4. Lastly, divide the total displacement (zero) by the total time (1 hour) to find the average velocity. Since the displacement is zero, the average velocity for the entire trip is also zero.
Therefore, the average velocity for the entire trip is 0 km/h.
b) Average speed for the entire trip:
To find the average speed, we divide the total distance traveled by the total time taken, irrespective of direction.
1. Calculate the total distance traveled during each segment, as we did for average velocity:
- First segment: 70 km
- Second segment: 15 km
- Third segment: 30 km
2. Calculate the total time taken, as we did for average velocity:
- Total time taken: 60 min, or 1 hour.
3. Divide the total distance traveled (70 km + 15 km + 30 km = 115 km) by the total time taken (1 hour) to find the average speed:
Average speed = Total distance / Total time = 115 km / 1 hour = 115 km/h.
Therefore, the average speed for the entire trip is 115 km/h.