A racing car starts from rest at t=0 and reaches a final speed v at time t. If the acceleration of the car is constant during this time, which of the following statements are true? a) the average speed of the car is v/2; b) the car travels a distance vt; c) the magnitude of the acceleration of the car is v/t; d) the velocity of the car remains constant; or e) none of the statements is true

All true statements are shown: a) The average speed of the car is , c)The magnitude of the acceleration of the car is .

Explanation:

Let prove the validity of each statement:

a) The average speed of the car is .

The average speed () is defined by the following formula:

(1)

Where:

, - Initial and final speeds of the racing car.

If we know that and , then the average speed of the racing car:

The statement is true.

b) The car travels a distance .

Since the racing car is accelerating uniformly, the distance travelled by the car is represented by the following kinematic formula:

(2)

Where is the acceleration of the racing car, measured in meters per square second.

The statement is false.

c) The magnitude of the acceleration of the car is .

Since the racing car is accelerating uniformly, the velocity of the racing car is represented by the following kinematic formula:

(3)

Then, we clear the acceleration of the expression:

If we know that and , then the acceleration of the car is:

The statement is true.

d) The velocity of the car remains constant.

Since the car accelerates uniformly, the vehicle does not travel at constant velocity.

The statement is false.

a longitudinal wave moves energy that is to the direction of the wave’s movement. - true