A mouse is running away from a cat at. 75 m/s and, at 1.25 m from his mouse hole, he accelerates at a constant rate of. 25 m/s^2 until he reaches his hole safely. How long a time was required for him to cover te last 1.25m?
To find the time required for the mouse to cover the last 1.25 m, we can use the kinematic equation:
\(s = ut + \frac{1}{2}at^2\),
where:
- \(s\) represents the displacement (1.25 m),
- \(u\) represents the initial velocity (75 m/s),
- \(a\) represents the acceleration (-0.25 m/s^2),
- \(t\) represents the time we want to find.
We rearrange the equation to solve for \(t\):
\(t = \sqrt{\frac{2s}{a}}\).
Substituting the given values, we find:
\(t = \sqrt{\frac{2 \times 1.25}{-0.25}}\).
Evaluating the expression:
\(t = \sqrt{-10}\).
Since the square root of a negative number is not real, it means the last part of the motion (covering the last 1.25 m) is not physically possible under the given conditions.