To find the time it takes for the car to achieve the final velocity, we can use the equation:
v = u + at
where v is the final velocity (25 m/s), u is the initial velocity (15 m/s), a is the acceleration (which is assumed to be constant), and t is the time taken.
Rearranging the equation, we have:
t = (v - u) / a
Plugging in the given values:
t = (25 m/s - 15 m/s) / a
To determine the acceleration, we can use the equation:
a = (v - u) / t
Plugging in the given values:
a = (25 m/s - 15 m/s) / t
Since the acceleration is constant, we can set both equations equal to each other:
(25 m/s - 15 m/s) / t = a
Simplifying the equation, we have:
10 m/s / t = a
Now, we can substitute this expression for acceleration into the time equation:
t = (25 m/s - 15 m/s) / (10 m/s / t)
Simplifying further:
t = (25 m/s - 15 m/s) * (t / 10 m/s) t = 10 m/s * (t / 10 m/s) t = t
As we can see, the time taken to achieve the final velocity cancels out, so it is independent of the acceleration.
Therefore, the time it takes for the car to achieve a final velocity of 25 m/s is the same as the time it takes to cover the given distance of 125 meters, which can be calculated using the formula:
t = d / u
where d is the distance traveled (125 m) and u is the initial velocity (15 m/s).
Plugging in the values:
t = 125 m / 15 m/s t ≈ 8.33 s
Therefore, it takes approximately 8.33 seconds for the car to achieve a velocity of 25 m/s.