Standard +0.3 This is a standard M2 mechanics problem requiring resolution of forces (weight, normal reaction, friction), application of F=ma, and use of kinematic equations. While it involves multiple steps (finding friction force, net deceleration, then distance using v²=u²+2as), the setup is routine and all techniques are directly applicable without requiring problem-solving insight or novel approaches.
2 A particle of mass \(m \mathrm {~kg}\) is projected directly up a rough plane with a speed of \(5 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). The plane makes an angle of \(30 ^ { \circ }\) with the horizontal and the coefficient of friction is 0.2 . Calculate the distance the particle travels up the plane before coming instantaneously to rest.
2 A particle of mass $m \mathrm {~kg}$ is projected directly up a rough plane with a speed of $5 \mathrm {~m} \mathrm {~s} ^ { - 1 }$. The plane makes an angle of $30 ^ { \circ }$ with the horizontal and the coefficient of friction is 0.2 . Calculate the distance the particle travels up the plane before coming instantaneously to rest.
\hfill \mbox{\textit{OCR M2 2008 Q2 [6]}}