Question

please help me solve this question...A car of mass m and a van of mass 2m travel at the speed.They are brought to rest by the same breaking force.What is the ratio of the distance travelled by the van to that of the car?

Answer 1

Please note that this is not the absolute way to solve the question. This is how I do it
So I assume the only net force acting on both object is just the breaking force.
\[F _{net}=m(-a)\] Note that the negative signs means deceleartion.
The question states that both cars were acted by the same net force. So,
\[F_{net of CAR}=F_{net of Van}\]\[m(-a)_{CAR}=2m(-a)_{VAN}\]\[\frac{ -a_{CAR} }{ -a_{VAN} }=\frac{ 2m }{ m }\]
By using linear motion equation
\[v^{2}=v_{0}^{2}+ 2ax\] note that v=0 and \[v_{0}^{2} \]the initial sped is the same for both vehicles. so we can deduce that
\[-2a_{CAR}x_{CAR}= -2a_{VAN} x_{VAN}\]\[-2(1) x_{CAR}=-2(2)x_{VAN}\]\[\frac{ x_{CAR} }{ x_{VAN} }=\frac{ 2 }{ 4 }=\frac{ 1 }{ 2 }\] so the ratio
x car : x van= 2:1

Answer 2

Ok...Thanks for your help...