a bus is travelling on a horizontal road at a velocity of 126 km/h when the bus driver notices an object in the road. the brakes are applied and the bus is brought to rest over a distance of 150m. the frictional resistance is 2500n and the bus has a mass of 6000 kg. calculate the retardation of the bus,the time taken to come to a stand still and the braking force of the brakes
a bus is travelling on a horizontal road at a velocity of 126 km/h when the bus driver notices an object in the road. the brakes are applied and the bus is brought to rest over a distance of 150m. the frictional resistance is 2500n and the bus has a mass of 6000 kg. calculate the retardation of the bus,the time taken to come to a stand still and the braking force of the brakes
To calculate the retardation of the bus, we can use the equation:
Retardation (a) = (Final Velocity^2 - Initial Velocity^2) / (2 * Distance)
First, we need to convert the velocity from km/h to m/s:
Initial Velocity = 126 km/h * (1000 m / 1 km) * (1 h / 3600 s)
Initial Velocity = 35 m/s
Next, we can use the given information to calculate the final velocity (0 m/s), and distance (150 m).
Retardation (a) = (0^2 - 35^2) / (2 * 150)
Retardation (a) = (-1225) / 300
Retardation (a) = -4.083 m/s^2
The negative sign indicates that the bus is decelerating.
To calculate the time taken to come to a standstill, we can use the equation:
Time (t) = (Final Velocity - Initial Velocity) / Retardation
Time (t) = (0 - 35) / (-4.083)
Time (t) = 8.57 seconds (rounded to two decimal places)
Finally, to calculate the braking force, we can use Newton's second law of motion:
Force (F) = Mass (m) * Acceleration (a)
Force (F) = 6000 kg * (-4.083 m/s^2)
Force (F) = -24500 N
Again, the negative sign indicates that the force is in the opposite direction of motion, i.e., against the motion of the bus. Therefore, the magnitude of the braking force is 24500 N.