a car running at 72 km h is slowed down to 18 km/h over a distance of 40m calculate :(1) retardation produced by brakes
To calculate the retardation produced by the brakes, we need to use the formula:
Retardation = (Initial velocity - Final velocity) / Time
In this case, the initial velocity is 72 km/h, the final velocity is 18 km/h, and the distance is 40 m. However, since the initial and final velocities are given in km/h and the distance is given in meters, we need to convert the velocities to m/s.
To convert km/h to m/s, we divide the value by 3.6. So, the initial velocity is 72 km/h / 3.6 = 20 m/s, and the final velocity is 18 km/h / 3.6 = 5 m/s.
Now we can calculate the time using the formula:
Distance = Initial velocity * Time - (1/2) * Retardation * Time^2
Rearranging the formula to solve for time:
Retardation * Time^2 - Initial velocity * Time + Distance = 0
Plugging in the values:
Retardation * Time^2 - 20 * Time + 40 = 0
Now we can solve this quadratic equation to find the value of time.
Once we know the value of time, we can plug it back into the initial formula to calculate the retardation.