A car of mass 760kg travel with a velocity of 14.0ms-1 . If the brakes are applied , the car travels a distance of 55.0m before coming to rest . Calculate the retarding force on the car
We can use the equation:
v^2 = u^2 + 2as
where v = 0 (final velocity), u = 14.0 ms^-1 (initial velocity), s = 55.0 m (distance), and a is the acceleration.
Rearranging the equation, we get:
a = (v^2 - u^2) / 2s
a = (0^2 - 14.0^2) / (2 x 55.0)
a = -7.63 ms^-2 (the negative sign indicates that the acceleration is in the opposite direction to the initial velocity)
Now, we can use Newton's Second Law of Motion, which states that:
Force = mass x acceleration
Substituting the values, we get:
Force = 760 kg x (-7.63 ms^-2)
Force = -5801.6 N
The retarding force on the car is 5801.6 N, which is directed opposite to the car's initial velocity.
To calculate the retarding force on the car, we will use the equation:
retarding force = mass x acceleration
First, we need to find the acceleration of the car. We can use the formula:
acceleration = (final velocity^2 - initial velocity^2) / (2 x distance)
Given:
Mass (m) = 760 kg
Initial velocity (u) = 14.0 m/s
Final velocity (v) = 0 (since the car comes to rest)
Distance (s) = 55.0 m
Now let's substitute the values into the formula and calculate the acceleration:
acceleration = (0^2 - 14.0^2) / (2 x 55.0)
acceleration = (-196) / 110
acceleration = -1.78 m/s^2
Now we can substitute the acceleration and mass into the formula to calculate the retarding force:
retarding force = 760 kg x (-1.78 m/s^2)
retarding force ≈ -1352.8 N
Therefore, the retarding force acting on the car is approximately -1352.8 N. The negative sign indicates that the force is acting in the opposite direction to the motion of the car, as it is a retarding force.