A bus traveling 85 km/hr is brought to a stop in 135 m. If the mass of the bus is 2250 kg, what was the retarding force provided by the brakes?
Formula please
10
To find the retarding force provided by the brakes, we can use Newton's second law of motion:
Force = mass × acceleration
In this case, the acceleration is given by the change in velocity divided by the time taken to stop. Since the bus is brought to a stop, the change in velocity is equal to the initial velocity. Therefore, the acceleration can be calculated as follows:
Acceleration = (change in velocity) / (time taken to stop)
Now, we need to find the change in velocity. The initial velocity is given as 85 km/hr, but we need to convert it to m/s, since the other units are in meters.
1 km/hr = (1000 m)/(3600 s) = 1/3.6 m/s
So, the initial velocity in m/s is:
Initial velocity = 85 km/hr × (1/3.6 m/s) = (85/3.6) m/s
Next, we need to find the time taken to stop. Since we know the distance traveled (135 m) and the initial velocity, we can use the equation of motion:
distance = (initial velocity × time) + (0.5 × acceleration × time^2)
In this case, the final velocity is 0, since the bus comes to a stop. Therefore, the equation can be simplified to:
distance = (initial velocity × time)
Plugging in the values, we get:
135 m = (85/3.6) m/s × time
Now, we can solve for time:
time = 135 m / ((85/3.6) m/s)
Once we have the time taken to stop, we can calculate the acceleration:
Acceleration = (change in velocity) / (time taken to stop) = (85/3.6) m/s / time
Finally, we can calculate the retarding force using Newton's second law:
Force = mass × acceleration = 2250 kg × (85/3.6) m/s / time
Therefore, the retarding force provided by the brakes is (2250 kg × (85/3.6) m/s) / time.