A car travels 12 km West, 18 km South. What is the total car displacement? The car takes 10 minutes to travel from each initial position to final position. What is the average speed and velocity?
Since the two trip segments are perpendicular, total displacement is sqrt[12^2 + 18^2] = 21.63 km
Divide than by 1/3 hour for the average velocity, 64.9 km/h. The velocity direction is 56.3 degrees south of west (arctan 1.5)
The average speed is the distance travelled (in any direction) divided by 1/3 hour, or 30 km/(1/3) = 90 km/h
Could you pleas explain it further? Thanks ;)
What don't you understand?
what will i divide by 1/3? And why should I divide it by 1/3?
And where did you get 64.9? Is that the velocity or what?
Divide the displacement (21.63 km) by 1/3 hour, to get the velocity. 1/3 hour is the twenty minutes elapsed time. You presumably want the velocity in km/h, so time must be in hours, not minutes.
The result of the division to get average velocity will be 64.9 km/h, as indicated.
Average velocity is displacement diovided by the time interval.
To find the total car displacement, you need to calculate the straight-line distance between the initial and final positions of the car. In this case, the car travels 12 km west and 18 km south.
To find the straight-line distance, you can use the Pythagorean theorem. The theorem states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the westward distance of 12 km can be considered as the "opposite" side, and the southward distance of 18 km can be considered as the "adjacent" side.
To calculate the displacement, you can use the formula:
displacement = √(westward distance^2 + southward distance^2)
displacement = √(12^2 + 18^2) = √(144 + 324) = √468 = 21.63 km (rounded to two decimal places)
Therefore, the total car displacement is 21.63 km.
Next, to find the average speed, you need to calculate the total distance traveled by the car divided by the total time taken. The car travels a total distance of 12 km + 18 km = 30 km.
Since the car takes 10 minutes to travel from each initial position to the final position, the total time taken is 10 minutes + 10 minutes = 20 minutes.
To find the average speed, you can use the formula:
average speed = total distance / total time
average speed = 30 km / 20 minutes = 1.5 km/minute.
Therefore, the average speed of the car is 1.5 km/minute.
Finally, to find the velocity, you need to consider the direction of the car. Velocity is a vector quantity that includes both magnitude and direction. In this case, the car travels 12 km west and 18 km south.
The magnitude of the velocity is the same as the average speed, which is 1.5 km/minute.
The direction of the velocity can be found by considering the displacement. Since the car is traveling to the west and then to the south, the direction of the velocity can be described as "21.63 km in a southwest direction".
Therefore, the average velocity of the car is 1.5 km/minute in a southwest direction.