a test car of mass 1250 kg is traveling at a speed of 72 kmph, when it is suddenly braked by locking the wheels. the average vehicle comes to a stop in a distance of 50 m. skid resisting force is.
72km/h=20m/s
acceleration=-vo^2/2*d
acceleration=-20^2/100
acceleration=-4m/s^2
F=m*a
F=1250*-4
F=-5000 N
Oh, dear test car, suddenly taking its brakes so far! Let's calculate the skid resisting force from this bizarre sequence of events.
To start the calculation, we need to convert the speed from km/h to m/s. Hold on tight, it's time for conversion madness!
72 km/h equals 20 m/s (approximately, rounding down for the sake of simplicity). Now that we've sorted that out, we can proceed.
To find the skid resisting force, we'll use the equation:
Force = (mass × acceleration)
But first, we need to find the acceleration. Ready? Here we go!
We can use the equation:
(v^2 - u^2) = 2as
Where:
v = final velocity (0 m/s, since the car comes to a stop)
u = initial velocity (20 m/s)
a = acceleration
s = distance covered (50 m)
Rearranging the equation, we have:
a = (v^2 - u^2) / (2s)
Plugging in the values, we get:
a = (0^2 - 20^2) / (2 × 50)
a = (-400) / 100
a = -4 m/s^2 (negative sign indicates deceleration)
Finally, we can calculate the skid resisting force:
Force = mass × acceleration
Force = 1250 kg × (-4 m/s^2)
Force = -5000 N
Voila! The skid resisting force is -5000 N (negative sign indicates it's opposing the vehicle's motion). It seems like a lot, but that's what happens when brakes are applied suddenly with locked wheels. Stay safe out there!
To find the skid resisting force, we can use the following equation:
\(F = m \cdot a\)
Where:
F = Skid resisting force
m = Mass of the car
a = Acceleration
First, let's convert the speed from km/h to m/s:
\(72 \, \text{km/h} = \frac{72}{3.6} \, \text{m/s} = 20 \, \text{m/s}\)
Now, let's calculate the acceleration using the following formula:
\(v^2 = u^2 + 2as\)
Where:
v = Final velocity (0 m/s, since the car comes to a stop)
u = Initial velocity (20 m/s)
a = Acceleration
s = Distance (50 m)
Rearranging the formula to solve for the acceleration:
\(a = \frac{{v^2 - u^2}}{{2s}}\)
Substituting the values:
\(a = \frac{{0^2 - 20^2}}{{2 \cdot 50}}\)
\(a = \frac{{-400}}{{100}}\)
\(a = -4 \, \text{m/s}^2\) (Negative sign indicates deceleration)
Finally, substituting the mass (m = 1250 kg) and the calculated acceleration (a = -4 m/s^2) into the skid resisting force equation:
\(F = m \cdot a\)
\(F = 1250 \, \text{kg} \cdot -4 \, \text{m/s}^2\)
\(F = -5000 \, \text{N}\) (The negative sign indicates that the force is acting in the opposite direction of motion)
Therefore, the skid resisting force is -5000 N.
To calculate the skid resisting force, we need to first determine the deceleration of the car. This can be done using the following formula:
Deceleration (a) = (Final Velocity^2 - Initial Velocity^2) / (2 * Distance)
First, let's convert the given speed from km/h to m/s since the unit of distance (meters) requires it.
Speed (v) = 72 km/h = (72 * 1000) / 3600 = 20 m/s
Given:
Mass (m) = 1250 kg
Initial Velocity (u) = 20 m/s (since the car suddenly brakes and comes to a stop)
Distance (s) = 50 m
Now we can calculate the deceleration:
a = (0^2 - 20^2) / (2 * 50)
a = (-400) / 100
a = -4 m/s^2
The negative sign indicates that the car is decelerating.
Next, we can calculate the skid resisting force (F) using Newton's second law of motion:
F = mass × acceleration
F = 1250 kg × (-4 m/s^2)
F = -5000 N (since force is negative, indicating resistance)
Therefore, the skid resisting force on the car is 5000 N.