Question

A car travels 30 miles in 1 hour on a winding mountain road. Which of the following is a true statement?

(A) The magnitude of the total displacement is larger than the distance traveled.
(B) The magnitude of the average velocity is greater than 30 m.p.h.
(C) The magnitude of the average velocity is equal to 30 m.p.h.
(D)The magnitude of the average velocity is less than to 30 m.p.h.
(E)The car traveled with a constant speed of 30 m.p.h.

Answer 1

Answer: The only true option is C

Step-by-step explanation:

A) because the car travels only in one direction, the total displacement (the difference of the final position and the initial position) is equal to the distance traveled. This option is false

B) The car moves at an average speed of exactly 30 miles per hour, this statement is false.

C) For the thing said before, this statement is correct, the average speed is equal to the total distance moved divided by the lapse of time, here the car moves 30 miles in one hour, so the average speed is 30 miles per hour

D) This can be true but not necessarily, the car may have varied the velocity, we know that the car moved 30 miles in the lapse of one hour, but maybe in some parts the velocity was 20mph and in other parts was 40mph, we do not really know, so this is false.

Answer 2

The true statement is:

"(C) The magnitude of the average velocity is equal to 30 m.p.h."

Step-by-step explanation:

Given that a car travels 30 miles in 1 hour on a winding mountain road.

Let' check all the statements one by one:

(A) The magnitude of the total displacement is larger than the distance traveled.

Since the entire motion of the car is not exactly given in the question, so it is not possible to tell whether the magnitude of the total displacement is larger than the distance traveled or not.

Thus, this statement is not true.

(B) The magnitude of the average velocity is greater than 30 m.p.h.

The average velocity of an object is defined as the total displacement covered by the particle divided by the total time taken in covering that displacement.

Total distance covered by the car = 30 miles.

Total time taken by the car to cover this distance = 1 hour.

Therefore, the average velocity of the car for this time interval =
`\rm (30\ miles)/(1\ hour )= 30\ m.p.h.`

Thus, this statement is also not true.

(C) The magnitude of the average velocity is equal to 30 m.p.h.

As is cleared in part (B) section above, the average velocity of the car in the given time interval is 30 m.p.h.

Thus, this statement is true.

(D)The magnitude of the average velocity is less than to 30 m.p.h.

Since. the average velocity of the car is 30 m.p.h.

Thus, this statement is not true.

(E)The car traveled with a constant speed of 30 m.p.h.

The motion of the car on the mountain road is not thoroughly given in the question, so again it is not possible to tell whether the car traveled with a constant speed of 30 m.p.h. or not.

Thus, this statement is also not true.