To solve this problem, we can break it down into two parts: the time taken to accelerate and the time taken to travel at a constant speed.
- Time taken to accelerate: The initial velocity, u, is 0 m/s (car starts from rest), and the acceleration, a, is 0.6 m/s^2. The time taken to accelerate, t_acc, can be calculated using the formula: t_acc = (v - u) / a
Plugging in the values: t_acc = (0.6 m/s - 0 m/s) / 0.6 m/s^2 t_acc = 1 second
- Time taken to travel at a constant speed: Once the car reaches its maximum speed, it continues at that speed. We need to find the distance traveled during this time. Let's call it d_const.
The formula to calculate distance, d, when the velocity, v, and time, t, are known is: d = v * t
Given that the maximum speed is 0.6 m/s and the time taken is 11 seconds, we can calculate the distance: d_const = 0.6 m/s * 11 s d_const = 6.6 meters
Now, we can find the total time taken to travel the first 75 meters by summing up the time taken to accelerate and the time taken to travel at a constant speed: Total time = t_acc + t_const
t_const is the time taken to travel the distance d_const at the constant speed, which can be calculated using the formula: t_const = d_const / v
Plugging in the values: t_const = 6.6 m / 0.6 m/s t_const ≈ 11 seconds
Therefore, the total time taken to travel the first 75 meters is: Total time = t_acc + t_const Total time = 1 second + 11 seconds Total time = 12 seconds