# Dynamic

#### Apprentice123

Determine the maximum theoretical speed expected for a car, leaving the rest, covering a distance of 50m. The coefficient of static friction between tire and road is 0,80. Knowing that the front wheels bear 60% of the weight of the car and the back, the remaining 40%. Determine the speed (a) traction front (b)
traction back

(a) 78,1 Km/h
(b) 63,8 Km/h

#### Deco

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Given:

$$\displaystyle \mu_s = 0.80$$
$$\displaystyle \Delta x= 50$$
$$\displaystyle V_i = 0$$

Solution:

$$\displaystyle F_f = \mu mg$$
$$\displaystyle F = ma$$
$$\displaystyle F= F_f$$
$$\displaystyle a= \mu g$$

$$\displaystyle V_{ff}^2-V_i^2 = (2\mu g\Delta x)(0.6)$$
$$\displaystyle \boxed{V_ff = 78.1 \mbox {km/h}}$$

and

$$\displaystyle V_{fb}^2-V_i^2 = (2\mu g\Delta x)(0.4)$$
$$\displaystyle \boxed{V_fb = 63.75 \mbox {km/h}}$$

Apprentice123