Question

Two cars A and B travelling towards each other on
a straight road with speed 20 ms 1 and 10 ms -1
respectively. When they are 400 m apart both drivers
apply brakes simultaneously and each car comes at
rest in the same time. The ratio of their magnitude
of retardations (an: ag) is​

Answer 1

Given:

Speed of A and B are given as

$u_{A}$=20 $ms^{-1}$

$u_{B}$=10 $ms^{-1}$

To Find: Ratio of their magnitude of retardation

Step by Step Solution:

Apply first equation of motion,

$v=u+at$

$0=u_{A}-a_{A}t$

solve the above equation

$a_{A}=\dfrac{u_{A} }{t} ----- (1)$

$0=u_{B}-a_{B}t$

solve the above equation

$a_{B}=\dfrac{ u_{B}}{t} -----(2)$

Divide equation (1) and equation (2)

$\dfrac{a_{A} }{a_{B} } =\dfrac{\dfrac{u_{A} }{t } }{\dfrac{u_{B} }{t} }=\dfrac{u_{A} }{u_{B} }=\dfrac{20}{10}=\dfrac{2}{1}$

The ratio of their magnitude of retardation is 2:1.