scooter is equal to the initial kinetic energy of the scooter.

The initial kinetic energy (KE) of the scooter can be given by:

$$ KE = \frac{1}{2} m v^2 $$

where

$$m$$ is the mass of the scooter
$$v$$ is the initial velocity of the scooter ($$7 \mathrm{~ms}^{-1}$$).

We are given that the scooter comes to a stop after traveling $$10 \mathrm{~m}$$, and the work done by the resistive force $$F$$ over this distance can be represented as:

$$ Work = F \cdot d $$

where

$$d$$ is the distance covered by the scooter before coming to a stop ($$10 \mathrm{~m}$$).

Therefore, the work done by the resistive force is equal to the initial kinetic energy:

$$ F \cdot d = \frac{1}{2} m v^2 $$

From Newton's second law, we also know that the weight of the scooter $$W$$ is given by:

$$ W = m g $$

thus, $$m = \frac{W}{g}$$

Substituting $$m$$ into the kinetic energy equation, we get:

$$ F \cdot 10 = \frac{1}{2} \left(\frac{W}{g}\right) \left(7\right)^2$$

Simplifying this equation:

$$ F \cdot 10 = \frac{1}{2} \left(\frac{W}{g}\right) \cdot 49 $$

$$ F = \frac{1}{2} \left(\frac{49 W}{10 g}\right) $$

$$ F = \frac{49 W}{20 g} $$

Given that gravity $$g = 9.8 \mathrm{~ms}^{-2}$$, we can substitute this value into the equation:

$$ F = \frac{49 W}{20 \cdot 9.8} $$

$$ F = \frac{49 W}{196} $$

$$ F = \frac{W}{4} $$

Therefore, the total resistance to the motion of the scooter is $$\frac{1}{4} W$$.

Thus, the correct answer is:

Option B: $$\frac{1}{4} W$$

Work Energy And Power

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