Question

A bus can be stopped by applying a retarding force F when it is moving with speed $v$ on a level road. The distance covered by it before coming to rest is s. If the load of the bus increases by $50\%$ because of passengers, for the same speed and same retarding force, the distance covered by the bus to come to rest shall be:

• A. $1.5s$
• B. $2s$
• C. $1s$
• D. $2.5s$

Answer 1

Answer: (A)

$1.5s$

Given retarding force = F

Initial velocity = V

Final velocity = 0

Distance covered before coming to rest = S

when load is increased by 50%

total mass $=\frac{1}{2}m+1m$

$=\frac{3}{2}m$

we know

$F=ma$

$\frac{F}{m}=a$ [$\therefore \frac{F}{m}$ = retarding force]

$\frac{F}{\frac{3}{2}m}=a$

$\frac{F}{m}=\frac{3}{2}a$

we know

Distance $\times$ acceleration

So,

$\frac{D_1}{D_2}=\frac{a_1}{a_2}$

$\frac{S}{S_2}=\frac{a_1}{a_2}$

$\frac{S}{S_2}=\frac{a}{\frac{3}{2}a}$

$S_2=1.5S$