To solve this problem, we need to determine how long the car was accelerating. We know the following details:
- The acceleration (a) of the car is 4.5 m/s².
- The total speed increase (Δv) is 99 m/s.
We can use the kinematic equation that relates acceleration, change in velocity, and time. The relevant formula here is:
[tex]\[ \Delta v = a \cdot t \][/tex]
Where:
- [tex]\(\Delta v\)[/tex] is the change in velocity,
- [tex]\(a\)[/tex] is the acceleration,
- [tex]\(t\)[/tex] is the time.
We need to find the time [tex]\(t\)[/tex]. We can rearrange the formula to solve for [tex]\(t\)[/tex]:
[tex]\[ t = \frac{\Delta v}{a} \][/tex]
Substituting the given values into the equation:
[tex]\[ t = \frac{99 \text{ m/s}}{4.5 \text{ m/s}^2} \][/tex]
By performing this division, we get:
[tex]\[ t = 22.0 \text{ seconds} \][/tex]
So, the car was accelerating for 22.0 seconds.
