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Question

A car of mass $1000kg$ is moving with a certain speed when a constant braking force $1000N$ acts on it for $5s$ and the speed of the car reduces to half its original speed. Find the further time required to stop the car if the same constant force acts.

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Solution

Step 1: Given data$Force\left(F\right)=1000N\phantom{\rule{0ex}{0ex}}Massofthecar\left(m\right)=1000kg\phantom{\rule{0ex}{0ex}}Initialtime\left(t\right)=5s$Step 2: Calculating initial velocityWe know that, $Force\left(F\right)=ma$Hence, $a=\frac{F}{m}=\frac{1000}{1000}=1m{s}^{-2}$Here the acceleration is equal to retardation. Therefore $a=-1m{s}^{-2}$.According to the first equation of motion, $v=u+at$Substitute $v=\frac{u}{2}$ (given that the speed of the car reduces to half its original speed).$\frac{u}{2}=u+\left(-1\right)×5\phantom{\rule{0ex}{0ex}}-\frac{u}{2}=-5⇒u=10m{s}^{-1}$Here the $Finalvelocity\left(v\right)=0$Speed of the car when braking $u=\frac{u}{2}=5m{s}^{-1}$.Step 3: Calculating the time required$v=u+at\phantom{\rule{0ex}{0ex}}0=5+\left(-1\right)×t\phantom{\rule{0ex}{0ex}}-5=-t\phantom{\rule{0ex}{0ex}}t=5s$Thus, the further time required to stop the car is $5s$.

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