Final answer:
The car accelerates from rest at 2.40 m/s² for 9.60 seconds, covering a distance of 110.592 meters.
Step-by-step explanation:
Calculating the Distance Travelled by an Accelerating Car
To calculate how far the car travels during its acceleration, we can use the kinematic equation for uniformly accelerated motion, which is:
d = vit + ½at²
Where d represents the distance traveled, vi is the initial velocity, t is the time, and a is the acceleration.
In this case, the car starts from rest, so the initial velocity (vi) is 0 m/s. Substituting the values given, we have:
d = 0 * 9.60s + ½(2.40 m/s²)(9.60 s)²
= 0 + ½(2.40)(92.16 s²)
= 1.20 * 92.16
= 110.592 m
Thus, the car travels a distance of 110.592 meters while it accelerates for 9.60 seconds.