Final answer:
The car accelerates from 5 m/s to 21 m/s at a rate of 3 m/s² and travels a distance of approximately 69.24 meters during this acceleration.
Step-by-step explanation:
To determine how far the car travels while accelerating, we can use the kinematic equation for uniformly accelerated motion, which is:
x = v0t + ½at²
However, we don't have the time (t) of the acceleration directly given. To find this, we can use the formula that relates velocity, acceleration, and time:
v = v0 + at
Here, v is the final velocity (21 m/s), v0 is the initial velocity (5 m/s), and a is the acceleration (3 m/s²). Rearrange this equation to solve for time (t):
t = (v - v0) / a
After finding the time, we can plug it back into the first equation to get the displacement (x).
Let's calculate the time first:
t = (21 m/s - 5 m/s) / 3 m/s²
= 16 m/s / 3 m/s²
= 5.33 s
Now, using the time value in the first equation:
x = (5 m/s)(5.33 s) + ½(3 m/s²)(5.33 s)²
= 26.65 m + ½(3 m/s²)(28.39 s²)
= 26.65 m + 1.5 m/s² × 28.39 s²
= 26.65 m + 42.59 m
= 69.24 m
The car travels 69.24 meters while accelerating.