Answer:
All true statements are shown: a) The average speed of the car is [tex]\frac{v}{2}[/tex], c)The magnitude of the acceleration of the car is [tex]\frac{v}{t}[/tex].
Explanation:
Let prove the validity of each statement:
a) The average speed of the car is [tex]\frac{v}{2}[/tex].
The average speed ([tex]\bar v[/tex]) is defined by the following formula:
[tex]\bar v = \frac{v_{o}+v_{f}}{2}[/tex] (1)
Where:
[tex]v_{o}[/tex], [tex]v_{f}[/tex] - Initial and final speeds of the racing car.
If we know that [tex]v_{o} = 0[/tex] and [tex]v_{f} = v[/tex], then the average speed of the racing car:
[tex]\bar v = \frac{0+v}{2}[/tex]
[tex]\bar v = \frac{v}{2}[/tex]
The statement is true.
b) The car travels a distance [tex]v\cdot t[/tex].
Since the racing car is accelerating uniformly, the distance travelled by the car is represented by the following kinematic formula:
[tex]x - x_{o}=v_{o}\cdot t + \frac{1}{2}\cdot a\cdot t^{2}[/tex] (2)
Where [tex]a[/tex] 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 [tex]\frac{v}{t}[/tex].
Since the racing car is accelerating uniformly, the velocity of the racing car is represented by the following kinematic formula:
[tex]v_{f} = v_{o}+a\cdot t[/tex] (3)
Then, we clear the acceleration of the expression:
[tex]a = \frac{v_{f}-v_{o}}{t}[/tex]
If we know that [tex]v_{o} = 0[/tex] and [tex]v_{f} = v[/tex], then the acceleration of the car is:
[tex]a = \frac{v-0}{t}[/tex]
[tex]a = \frac{v}{t}[/tex]
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.
