To determine the acceleration of a car that maintains a constant velocity of 300 m/s over the course of 30 seconds, we can follow these steps:
1. Understand the concepts involved:
- Velocity is the rate at which an object changes its position.
- Acceleration is the rate at which an object's velocity changes over time.
2. Given data:
- Final velocity ([tex]\( v_f \)[/tex]) = 300 m/s
- Initial velocity ([tex]\( v_i \)[/tex]) = 300 m/s (since the car maintains a constant velocity, the initial and final velocities are the same)
- Time ([tex]\( t \)[/tex]) = 30 s
3. Formula for acceleration:
- Acceleration ([tex]\( a \)[/tex]) is calculated using the formula:
[tex]\[
a = \frac{v_f - v_i}{t}
\][/tex]
4. Substitute the given values into the formula:
[tex]\[
a = \frac{300 \, \text{m/s} - 300 \, \text{m/s}}{30 \, \text{s}}
\][/tex]
5. Calculate the acceleration:
- Since the final velocity and initial velocity are the same (300 m/s), the numerator of the fraction becomes:
[tex]\[
300 \, \text{m/s} - 300 \, \text{m/s} = 0 \, \text{m/s}
\][/tex]
- Thus, the acceleration is:
[tex]\[
a = \frac{0 \, \text{m/s}}{30 \, \text{s}} = 0 \, \text{m/s}^2
\][/tex]
The acceleration of the car is [tex]\( 0 \, \text{m/s}^2 \)[/tex]. This result makes sense because the velocity is constant, meaning there is no change in velocity over time, and therefore no acceleration.
