A car moving with a speed of 50 km per hour can be stopped by brakes a...
Minimum Stopping Distance Calculation:
Given:
- Initial speed of the car, v1 = 50 km/h
- Stopping distance at this speed, d1 = 6 m
Step 1: Convert Initial Speed to m/s
- Initial speed in m/s, v1 = 50 km/h = 50 * 1000 / 3600 = 13.89 m/s
Step 2: Calculate Initial Stopping Distance
- Using the equation v^2 = u^2 + 2as, where u = initial velocity, v = final velocity (0 m/s), a = acceleration, s = stopping distance
- Rearranging the equation, we get s = v^2 / 2a
- Substituting the values, d1 = 13.89^2 / (2 * a)
- Solving for 'a', we get a = 13.89^2 / (2 * 6) = 38.36 m/s^2
Step 3: Calculate Minimum Stopping Distance at 100 km/h
- New speed of the car, v2 = 100 km/h = 100 * 1000 / 3600 = 27.78 m/s
- Using the same equation v^2 = u^2 + 2as, and the acceleration 'a' calculated above, we can find the new stopping distance
- d2 = 27.78^2 / (2 * 38.36) = 12.63 m
Therefore, the minimum stopping distance when the car is moving at a speed of 100 km/h is 12.63 meters.