# This Is A Mathematical Methods And Mechanics Problem Hope You Can Help Thanks

A block of mass m is given an initial velocity of Mo at a ﬁxed origin 0 and it began to
slide on a rough horizontal surface. At a position x from 0, it has a velocity of v. Take the magnitude of the acceleration due to gravity to be g and the coefﬁcient of sliding
friction to be ,u. (a) Deﬁne an appropriate coordinate axis, draw a force diagram of the block and
write down the vector form of all forces. (5 marks) (b) Apply Newtonian mechanics and present the equation of motion for the block.
(3 marks) (c) Show that the distance travelled by the block from the origin 0 is given by (4 marks) ((1) For no = 2 ms’1 and p! = 0.02, calculate the distance travelled by the block when
it comes to a stop. (2 marks) Now consider the effect of air resistance. The same block of mass m is given an initial
velocity of no at a ﬁxed origin 0 and it began to slide on a rough holizontal surface.
When sliding, the block now expeliences air resistance of magnitude A7152. (e) Apply Newtonian mechanics and solve an expression the distance travelled by
the block from the origin 0, in terms of m, am, y, k, v and g.
(7 marks} Science