Question 1.
A car moves 26 km due east then 14 km due north. It then turns along a path running north-east 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 formula is total distance divided by total time
average velocity formula is total displacement over time
the two may seem like the same thing but they arent
velocity is a vector so direction has to be taken into account (for example say you start at an inital position and move ;eft 1 meter and then move right one meter, your total distance is 2 meter but your total displacement is zero because you are right back where you started
for your speed just add your total distance traveled (26 + 14 +15 + 17) and divide that by 2 hours
the velocity for this is a little trickier you have to figure out your final position and how far you are from your starting point and divide that by the time
To find the car's average speed and average velocity, we need to break down the steps into individual parts and then calculate the total distance traveled and the total displacement.
Step 1: Analyzing the Movements
The car moves 26 km due east, then 14 km due north. It then turns along a path running northeast for 15 km and finally goes 17 km due west.
Step 2: Calculate the Total Distance Traveled
To find the total distance traveled, we need to sum up the distances covered in each step. The car covered 26 km east, 14 km north, 15 km northeast, and 17 km west. Thus, the total distance traveled is 26 + 14 + 15 + 17 = 72 km.
Step 3: Calculate the Total Displacement
To find the total displacement, we need to calculate the straight-line distance from the initial point to the final point. Visualization will help in understanding the movement.
The movements can be represented as a right-angled triangle, with the eastward and northward movements as the two legs of the triangle. Using the Pythagorean theorem, we can calculate the hypotenuse (total displacement).
The eastward movement (26 km) and northward movement (14 km) form a right-angled triangle. Using the Pythagorean theorem, the total displacement (D) can be calculated as follows:
D² = 26² + 14²
D² = 676 + 196
D² = 872
D ≈ 29.5 km
So, the total displacement is approximately 29.5 km.
Step 4: Calculate the Average Speed
Average speed is calculated by dividing the total distance traveled by the total time taken.
Average speed = Total distance / Total time
Given that the time for the entire journey is 2 hours and the total distance is 72 km, we can find the average speed:
Average speed = 72 km / 2 h
Average speed = 36 km/h
Therefore, the car's average speed is 36 km/h.
Step 5: Calculate the Average Velocity
Average velocity is calculated by dividing the total displacement by the total time taken. Velocity includes both the magnitude (distance) and the direction.
Average velocity = Total displacement / Total time
Given that the total displacement is 29.5 km and the total time is 2 hours, we can find the average velocity:
Average velocity = 29.5 km / 2 h
Average velocity = 14.75 km/h
Therefore, the car's average velocity is 14.75 km/h.
To summarize:
(a) The car's average speed is 36 km/h.
(b) The car's average velocity is 14.75 km/h.