1. A particle of mass m falls from rest, under gravity, in a medium in which...

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1. A particle of mass m falls from rest, under gravity, in a medium in which the resistance to its motion is mkv, where k is a constant and v is the speed of the particle. (i) (ii) (iv) (v) Write down the equation of motion for the particle. If the motion were to continue indefinitely, v would approach a constant value vt. (vi) Show that k (iii) Hence show that = 8 V₁ given by dv dt = V (In In 2 Show also that, during this time interval, the particle has fallen a distance s g Show that the particle is moving with velocity after a time - (v, – v) - dv - (In 2-1) Hence show that s = In 2 g (vii) Find the average speed, in the form 2 vt, during this time interval, expressing λ to 2 decimal places. 1. A particle of mass m falls from rest, under gravity, in a medium in which the resistance to its motion is mkv, where k is a constant and v is the speed of the particle. (i) (ii) (iv) (v) Write down the equation of motion for the particle. If the motion were to continue indefinitely, v would approach a constant value vt. (vi) Show that k (iii) Hence show that = 8 V₁ given by dv dt = V (In In 2 Show also that, during this time interval, the particle has fallen a distance s g Show that the particle is moving with velocity after a time - (v, – v) - dv - (In 2-1) Hence show that s = In 2 g (vii) Find the average speed, in the form 2 vt, during this time interval, expressing λ to 2 decimal places.