Final answer:
To calculate the distance a sports car covers while increasing its velocity from 7 to 13 m/s, first find the time using t = (v - vo) / a, then the distance using d = vo*t + 1/2*a*t². The car covers a distance of 19.5 meters.
Step-by-step explanation:
The question involves calculating the distance a sports car covers when its velocity increases from 7 m/s to 13 m/s with an acceleration of 4.0 m/s². To find the distance, we can use the kinematic equation d = vot + ½at², where d is the distance, vo is the initial velocity, a is the acceleration, and t is the time. However, we need to find the time first. Time can be calculated using the equation t = (v - vo) / a, where v is the final velocity.
First, let's find the time:
t = (13 m/s - 7 m/s) / 4.0 m/s² = 1.5 s
Now, let's calculate the distance using the initial velocity, time, and acceleration:
d = (7 m/s)(1.5 s) + ½(4.0 m/s²)(1.5 s)²
d = 10.5 m + 9 m
d = 19.5 m
The sports car covers a distance of 19.5 meters while increasing its velocity from 7 to 13 m/s with an acceleration of 4.0 m/s².