A race car moving at 35 m/s is uniformly slowed to a stop in 50 s. Find 1) acceleration, and 2) stopping distance.
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To find the acceleration, we can use the formula:
acceleration (a) = (final velocity - initial velocity) / time
Given:
- Initial velocity (u) = 35 m/s
- Final velocity (v) = 0 m/s
- Time (t) = 50 s
Using the formula, we can plug in the values:
acceleration (a) = (0 - 35) / 50
Simplifying the equation:
acceleration (a) = -35 / 50
Thus, the acceleration is -0.7 m/s² (negative sign indicates deceleration).
Now, to find the stopping distance, we can use the formula:
stopping distance = (initial velocity × time) + (1/2 × acceleration × time²)
Given:
- Initial velocity (u) = 35 m/s
- Time (t) = 50 s
- Acceleration (a) = -0.7 m/s²
Substituting the values into the formula:
stopping distance = (35 × 50) + (0.5 × -0.7 × 50²)
Simplifying the equation:
stopping distance = 1750 - 0.35 × 50²
Calculating further:
stopping distance = 1750 - 0.35 × 2500
stopping distance = 1750 - 875
stopping distance = 875 m
Therefore, the stopping distance is 875 meters.