# A soccer star is travelling with a car of a mass of 880kg on a horizontal road at a velocity of 30m/s. He immediately applies the brakes so as to stop 50m away. The resistance to motion on the horizontal road is 295N. Calculate the deceleration of the car and the braking force

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## V^2 = Vo^2 + 2a*d.

0 = 30^2 + 2a*50,
a = -9 m/s^2.

-F-Fk = M*a.
-F-295 = 880*(-9),
F = ?.

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## To calculate the deceleration of the car, we can use the following equation:

deceleration = (final velocity^2 - initial velocity^2) / (2 * distance)

Given:
Mass of the car (m) = 880 kg
Initial velocity (u) = 30 m/s
Final velocity (v) = 0 m/s (since the car is coming to a stop)
Distance (s) = 50 m

Using the formula, we can calculate the deceleration:

deceleration = (0^2 - 30^2) / (2 * 50)
deceleration = (-900) / 100
deceleration = -9 m/s^2

Now, to calculate the braking force, we can use Newton's second law of motion:

Force (F) = mass (m) * acceleration (a)

Given:
Mass of the car (m) = 880 kg
Acceleration (a) = deceleration = -9 m/s^2

Using the formula, we can calculate the braking force:

Force = 880 kg * (-9 m/s^2)
Force = -7920 N

The negative sign indicates that the force is acting in the opposite direction of motion, i.e., the braking force. Therefore, the braking force is 7920 N.

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## To find the deceleration of the car, we can use the equation:

Acceleration = (final velocity - initial velocity) / time taken

Since the car is coming to a stop, the final velocity will be 0 m/s. The initial velocity is given as 30 m/s.

To find the time taken, we can use the equation:

Distance = (initial velocity + final velocity) / 2 * time taken

We know the initial velocity and the distance, and we can rearrange the equation to solve for the time taken:

time taken = 2 * distance / (initial velocity + final velocity)

Using the given values, we have:

time taken = 2 * 50m / (30m/s + 0m/s)
= 2 * 50m / 30m/s
= 3.33s

Now that we have the time taken, we can find the acceleration:

Acceleration = (0m/s - 30m/s) / 3.33s
= -30m/s / 3.33s
= -9 m/s^2

The negative sign indicates that the car is decelerating, or slowing down.

To find the braking force, we can use Newton's second law of motion:

Force = mass * acceleration

We know the mass of the car is 880kg, and we just calculated the acceleration as -9 m/s^2.

Force = 880kg * (-9 m/s^2)
= -7920 N

The negative sign indicates that the force is acting in the opposite direction of the motion, which makes sense since the car is braking.

Therefore, the deceleration of the car is -9 m/s^2 and the braking force is -7920 N.