Average speed, displacement and average velocity of car.

[ntseg001]

A car travels 50km at 30degrees North of East for 20min, then 30km at 70degrees North of East with speed of 20km/hr, then another 10km at 60degrees North of East with speed 80km/hr. Find
A)Total distance traveled
B)The average speed of the car
C)The displacement of the car(magnitude and the angle relative to East)
D)The average velocity of the car.

 

[physics girl phd]

Hi ntseg001! Welcome to the forums! What is your work so far on this problem? (See forum rules... in order to get help, you need to show your efforts.)

 

[thomate1]

A) The total distance traveled by the car can be calculated by adding the distances traveled in each segment. In this case, the total distance would be 50km + 30km + 10km = 90km.

B) The average speed of the car can be calculated by dividing the total distance traveled by the total time taken. In this case, the total time taken would be 20 minutes (or 1/3 hour) + 30 minutes (or 1/2 hour) + 7.5 minutes (or 1/8 hour) = 0.875 hours. Therefore, the average speed would be 90km / 0.875 hours = 102.86 km/hr.

C) The displacement of the car can be calculated by finding the shortest straight-line distance from the starting point to the ending point. In this case, the car's displacement would be the hypotenuse of a right triangle with sides of 50km and 40km (30km + 10km). Using the Pythagorean theorem, the displacement would be √(50^2 + 40^2) = 64.03 km. The direction of the displacement can be found by using trigonometric functions, in this case, the angle would be tan^-1(40/50) = 38.66 degrees North of East.

D) The average velocity of the car is the displacement divided by the total time taken. In this case, the average velocity would be 64.03 km / 0.875 hours = 73.17 km/hr at an angle of 38.66 degrees North of East. This means that the car's average velocity is slightly slower than its average speed, as it had to make turns and changes in direction during its journey.