Question

what net braking force must be applied to stop a car with mass of 900kg initially travelliing at velocity of 100kmh-1 within a straight line distance of 50m?

Answer 1

what net braking force must be applied to stop a car with mass of 900kg initially travelling at velocity of 100kmh-1 within a straight line distance of 50m?

Solution:

$m = 900kg$ - mass of the car;

$V = 100\frac{km}{h} \approx 27.8\frac{m}{s}$ - the initial speed of the car;

$S = 50m$ - braking distance;

$a$ - deceleration of the car.

Equations of motion for the car on the X-axis:

$$S = V t - \frac {a t ^ {2}}{2}$$

Rate equation for the car along the X-axis

$$0 = V - a t$$ $$t = \frac {V}{a}$$

(2)in (1):

$$S = V \cdot \frac {V}{a} - \frac {a V ^ {2}}{2 a ^ {2}}$$ $$S = \frac {V ^ {2}}{2 a}$$ $$a = \frac {V ^ {2}}{2 S}$$

Hence, we have acceleration, so we can now use Newton's second law (the projection on the X-axis) for the car:

$$\vec {F} = m \vec {a}$$ $$x: F = m a$$

(3)in(4):

$$F = \frac {m V ^ {2}}{2 S} = \frac {9 0 0 k g \cdot \left(2 7 . 8 \frac {m}{s}\right) ^ {2}}{2 \cdot 5 0 m} = 6 9 5 0 N$$

Answer: net braking force is 6950N.