Question

a motor vehicle of mass 800kg stands on an incline where gradient is 1 in 10. the handbrake is released and the vehicle runs down the incline. if the resistance to motion is 40 N., find the speed of the vehicle after running 200m down the incline

Answer 1

\[mgsin \theta - R=ma \rightarrow a=gsin \theta -\frac{ R }{ m }\]\[v=at\]\[s=\frac{ at^2 }{ 2 } \rightarrow t=\sqrt{\frac{ 2s }{a }}\]\[v=a \sqrt{\frac{ 2s }{ a }}=\sqrt{2as}=\sqrt{2s*(gsin \theta -\frac{ R }{m })}\]
\[\sin \theta= \frac{ 1 }{10 }\]
\[v=\sqrt{2*200*(1-0,05)}=\sqrt{400*0,95}=19,5\]