Question

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

Answer 1

Answer:

All true statements are shown: a) The average speed of the car is $\frac{v}{2}$, c)The magnitude of the acceleration of the car is $\frac{v}{t}$.

Explanation:

Let prove the validity of each statement:

a) The average speed of the car is $\frac{v}{2}$.

The average speed ($\bar v$) is defined by the following formula:

$\bar v = \frac{v_{o}+v_{f}}{2}$ (1)

Where:

$v_{o}$, $v_{f}$ - Initial and final speeds of the racing car.

If we know that $v_{o} = 0$ and $v_{f} = v$, then the average speed of the racing car:

$\bar v = \frac{0+v}{2}$

$\bar v = \frac{v}{2}$

The statement is true.

b) The car travels a distance $v\cdot t$.

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

$x - x_{o}=v_{o}\cdot t + \frac{1}{2}\cdot a\cdot t^{2}$ (2)

Where $a$ 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 $\frac{v}{t}$.

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

$v_{f} = v_{o}+a\cdot t$ (3)

Then, we clear the acceleration of the expression:

$a = \frac{v_{f}-v_{o}}{t}$

If we know that $v_{o} = 0$ and $v_{f} = v$, then the acceleration of the car is:

$a = \frac{v-0}{t}$

$a = \frac{v}{t}$

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.