A car of mass 760kg travels with a velocity of 14ms-1
If the brakes are applied,the car travels a distance of 55m before coming to rest.
Calculate the retarding force on the car
Well, if you're asking for the retarding force, I guess the car wasn't too excited about coming to a stop. It must have thought, "Brakes? Not my favorite thing, but I guess I'll cooperate." Now let's calculate that force.
Using the formula for force, we have:
Force = (mass * change in velocity) / time
Now, since the car comes to rest, the change in velocity is simply its initial velocity, which is 14 m/s, and the time taken is unknown. However, we know that the car travels a distance of 55 meters. This brings us to the equation:
distance = (initial velocity * time) + (0.5 * acceleration * time^2)
Since the car comes to rest, the final velocity is 0. Rearranging the equation, we get:
time = (2 * distance) / initial velocity
Plugging in the values, we find:
time = (2 * 55) / 14 = 7.857 seconds
Now we can calculate the force:
Force = (mass * change in velocity) / time
= (760 kg * 14 m/s) / 7.857 s
= 1367.6 N
So, the retarding force on the car is approximately 1367.6 Newtons.
To calculate the retarding force on the car, we can use the equation of motion:
v^2 = u^2 + 2as
Where:
v = final velocity (0 m/s, as the car comes to rest)
u = initial velocity (14 m/s)
a = acceleration (retarding force/mass)
s = distance traveled (55 m)
Rearranging the equation, we can solve for the acceleration:
a = (v^2 - u^2) / (2s)
Substituting the given values:
a = (0^2 - 14^2) / (2 * 55)
a = (-196) / 110
a ≈ -1.78 m/s^2
The negative sign indicates that the force is opposite to the direction of motion, acting as a retarding force.
The retarding force can be calculated using Newton's second law, F = ma:
F = (760 kg * -1.78 m/s^2)
F ≈ -1352.8 N
So, the retarding force on the car is approximately -1352.8 N.
To calculate the retarding force on the car, we can use Newton's second law of motion. According to this law, the force acting on an object is equal to the mass of the object multiplied by its acceleration. In this case, the acceleration of the car can be calculated using the kinematic equation:
vf^2 = vi^2 + 2ad
Where:
- vf is the final velocity, which is 0 m/s since the car comes to rest
- vi is the initial velocity, given as 14 m/s
- a is the acceleration
- d is the distance traveled, given as 55 m
Rearranging the equation to solve for acceleration, we have:
a = (vf^2 - vi^2) / (2d)
Since vf^2 = 0 and vi^2 = 14^2, the equation becomes:
a = (-14^2) / (2 * 55)
Calculating this, we find:
a ≈ -4.12 m/s^2
The negative sign indicates that the acceleration is in the opposite direction of motion, corresponding to the deceleration caused by the brakes.
Finally, to find the retarding force, we can multiply the mass of the car (760 kg) by the acceleration (-4.12 m/s^2):
F = m * a
F = 760 kg * -4.12 m/s^2
Calculating this, we find:
F ≈ -3147.2 N
Therefore, the retarding force on the car is approximately -3147.2 N. The negative sign indicates that the force is opposing the motion of the car.
the stopping time (t) is ... 55 m / (14 m/s / 2)
the stopping deceleration (a) is ... 14 m/s / t
f = m a