• A car moves 26 km due east then 14 km due north. It then turns along a path running north-west with 15 km, then 17 km due west. If the time for the entire journey is 2 hrs.
• Find;
• (a) the car’s average speed in m/s
• (b) the car’s average velocity in km/h
Average speed = (26+14+15+17)/2 km/h
=36 km/h
=36x1000/(60x60) m/s
=10 m/s
(a) For the average speed, divide the total distance travelled, in ANY direction, by 2 hours. That would result in:
(26 + 14 + 15 + 17)/2 = 36 km/h = 36000 m/3600 s = 10.0 m/s
(b) For the average velocity, divide the distance between the starting and finishing points (a vector sum) by 2 hours.
The vector velocity from start to finish is
(26i + 14j -10.607i + 10.607j -17i)/2
= (1.607i -24.607j)/2
(i represents the east direction and j represents the north direction)
= 0.803 i -12.304 j
The magnitude of the average velocity (average speed) is 12.33 km/h, and the direction is slightly north of west.
Simple question
:D
To find the car's average speed and average velocity, we need to use the formulas:
Average Speed = Total Distance / Total Time
Average Velocity = Displacement / Total Time
(a) First, let's calculate the car's average speed in m/s. We'll use the formula average speed = total distance / total time.
The car moves 26 km east, 14 km north, 15 km northwest, and 17 km west. To calculate the total distance, we need to calculate the length of the path the car has taken.
Using the Pythagorean theorem, we can find the length of the north-west path:
Length = sqrt(15^2 + 17^2)
Distance = 26 km + 14 km + Length
Total Time = 2 hours
Average Speed = (26 km + 14 km + Length) / 2 hours
Now, let's convert the answer to m/s. Remember, 1 km/hr = 1000 m/3600 s.
Average Speed (m/s) = (Distance in meters) / (Total Time in seconds)
(b) To find the car's average velocity in km/h, we need to calculate the displacement and then divide it by the total time.
The displacement is the straight-line distance and direction from the starting point to the final point. We'll use vector addition to calculate it.
The car moves 26 km east and 14 km north. To calculate the displacement, we can draw a right triangle to find the resultant vector.
Let's consider the east direction as the positive x-axis and the north direction as the positive y-axis.
The x-component of the displacement is the sum of the eastward distances (26 km) and the westward distances (-17 km).
The y-component of the displacement is the sum of the northward distances (14 km) and the southward distances (0 km).
Displacement = sqrt(x_component^2 + y_component^2)
Total Time = 2 hours
Average Velocity = Displacement / Total Time
Now, let's convert the answer to km/h by multiplying by 3600/1000.
Average Velocity (km/h) = (Displacement in km) / (Total Time in hours)