A car accelerates from 12.5 m/s to 25 m/s in 6.0 seconds. What was the acceleration?
The correct answer and explanation is :
To calculate the acceleration of the car, we can use the formula for acceleration:
[
a = \frac{{v_f – v_i}}{{t}}
]
Where:
- (a) is the acceleration,
- (v_f) is the final velocity,
- (v_i) is the initial velocity,
- (t) is the time.
Given values:
- Initial velocity, (v_i = 12.5 \, \text{m/s}),
- Final velocity, (v_f = 25.0 \, \text{m/s}),
- Time, (t = 6.0 \, \text{seconds}).
Step-by-step calculation:
Substitute the given values into the formula:
[
a = \frac{{25.0 \, \text{m/s} – 12.5 \, \text{m/s}}}{{6.0 \, \text{seconds}}}
]
[
a = \frac{{12.5 \, \text{m/s}}}{{6.0 \, \text{seconds}}}
]
[
a = 2.083 \, \text{m/s}^2
]
Conclusion:
The acceleration of the car is 2.08 m/s² (rounded to two decimal places).
Explanation:
Acceleration is the rate at which an object’s velocity changes over time. In this problem, the car’s initial velocity is 12.5 m/s, and it increases to 25.0 m/s over a period of 6.0 seconds. To find the acceleration, we look at how much the velocity changes, which is the difference between the final and initial velocities. The formula used is straightforward, and it relates the change in velocity to the time taken for that change.
In this case, the velocity increases by 12.5 m/s (from 12.5 m/s to 25.0 m/s) over 6 seconds, so the car is accelerating at a rate of 2.08 m/s². This means that every second, the car’s velocity increases by 2.08 meters per second. Acceleration is a vector quantity, meaning it has both magnitude and direction, but since the problem does not specify a direction, we assume the acceleration is in the same direction as the car’s motion.