Question 48: Solution
1. Analysis of Forces at Start
The car starts from rest ($v=0$). At this instant, the resistive air drag force ($F_{drag} = bv$) is zero. The only horizontal force providing acceleration is the traction from the tires.
Since the wheels are “maintained always at the verge of slipping,” the traction force is the maximum static friction:
$$ F_{net} = f_s – F_{drag} $$
$$ ma = \mu mg – bv $$
At $t=0$, $v=0$:
$$ ma_{initial} = \mu mg \implies a_{initial} = \mu g $$
2. Calculation from Graph
The problem states the graph is linear in the first 10 seconds. We calculate the slope ($a$) using the points $(0,0)$ and $(10, 10)$:
$$ a = \frac{\Delta v}{\Delta t} = \frac{10 – 0}{10 – 0} = 1 \, \text{m/s}^2 $$
Substituting this back into our force equation (assuming $g \approx 10 \, \text{m/s}^2$):
$$ \mu g = 1 $$
$$ \mu (10) = 1 $$
$$ \mu = 0.10 $$
Correct Option: (c) 0.10