Final answer:
To find the distance traveled by the car while accelerating from rest, we can use the equation d = (3/2)t^2, where d is the distance traveled and t is the time taken. The equation shows that the distance traveled is directly proportional to the square of the time taken.
Step-by-step explanation:
The given problem involves a car accelerating from rest at a constant rate. To find the distance traveled, we can use the equation:
d = vit + (1/2)at2
Where:
d = distance traveled
vi = initial velocity (0 m/s since it starts from rest)
t = time taken
a = acceleration (given as 3.0 m/s²)
Since the final speed is not given, we're only interested in the distance traveled while accelerating. The final speed will be used to calculate the deceleration distance, which is not needed for this question.
Now we can plug in the known values to solve for the distance traveled:
d = (0 m/s)(t) + (1/2)(3.0 m/s²)(t2)
Simplifying the equation:
d = (3/2)t2
Therefore, the distance traveled while accelerating is directly proportional to the square of the time taken.