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.

d.7.5cm is your answer

when jerome paddle in flowing river towards east the net speed of jerome will increase

so the net speed of jerome will be given as

now the speed of paul will be same as it is given as he is running on the ground

so

so here we can say since the speed of jerome is more so he will win the race

now as we know the distance so the time difference is given as

so jerome will reach first and the time difference will be 203.55 s or 3.4 min