COMEDK 2024 Shift 2 Paper

To determine the total resistance to the motion of the scooter, we can start by using the workenergy principle. According to this principle, the work done by the resistive forces to stop the scooter is equal to the initial kinetic energy of the scooter.
The initial kinetic energy (KE) of the scooter can be given by:
KE=‌

1

2

mv2
where
m is the mass of the scooter
v is the initial velocity of the scooter (7ms−1).
We are given that the scooter comes to a stop after traveling 10 m , and the work done by the resistive force F over this distance can be represented as:
‌ Work ‌=F⋅d
where
d is the distance covered by the scooter before coming to a stop (10m).

Therefore, the work done by the resistive force is equal to the initial kinetic energy:
F⋅d=‌

1

2

mv2
From Newton's second law, we also know that the weight of the scooter W is given by:
W=mg
thus, m=‌

W

g

Substituting m into the kinetic energy equation, we get:
F⋅10=‌

1

2

(‌

W

g

)(7)2
Simplifying this equation:
‌F⋅10=‌

1

2

(‌

W

g

)⋅49
‌F=‌

1

2

(‌

49W

10g

)
‌F=‌

49W

20g

Given that gravity g=9.8ms−2, we can substitute this value into the equation:
‌F=‌

49W

20⋅9.8

‌F=‌

49W

196

‌F=‌

W

4

Therefore, the total resistance to the motion of the scooter is ‌

1

4

W.
Thus, the correct answer is:
Option B: ‌

1

4

W