My usual policy of not giving you exact answers but reasoning applies here.

The questions also seem to be about as well written as a usual question of this type and requires several rather large assumptions (which you should state and maybe even explain: if nothing else it goes to method marks).

I have assumed this question is of a level that would normally be taught to 16 year olds through to first year of an engineering degree but tell me if it is any different here.

I am assuming it accelerates to 6 m/s over the course of the 14m. Acceleration must be linear as no function is given for anything meaning basic equations of linear motion. My symbols might be different so

s= displacement

t=time

v=final velocity

u=initial velocity

a= acceleration.

v2 =u2 +2as here as you have no time value

s= ut +1/2at^2 or its cousin s= vt - 1/2at^2, it does not really matter as you have v and u. You will end up with a quadratic to solve here.

Here I would read on and determine what I needed for the later questions and write it down but do it however you like. You might like to draw a diagram too as some of this has the potential to cause issues because you are going to be rearranging equations where sign counts.

**1)** I assume this means calculate the energy expended during the course of movement.

break it down and add it up (1st law of thermodynamics referenced there tells you this). Work done = energy. The components here being gravity and friction.

work against gravity

Yawn, gravitational potential energy that I assume you have done several times before.

weight.height = m.g.h = work against gravity

work against friction

I assume friction is constant, what sort of resistance it is at this point is entirely inconsequential.

Extra force would have to be provided to overcome friction.

force.distance moved= work done. Force given friction does not seem to be causing acceleration = friction (albeit in the opposite direction so I should really say equal in magnitude).

**2)** an odd one. Normally such a question is posed with multiple angled threads to determine weight and it is assumed the acceleration is near 0 (not to mention the maths gets fairly complex). The cable I assume is light and inextensible (again it does not make the maths nice).

For this reason I assume it is simply the mass having been suspended and the tension now measured.

Resistance **to motion** is mentioned but as I have assumed this is a stationary object I am willing to neglect it (it is a simple extra step when resolving forces anyhow), if it says it is friction (from a shaft of something) rather than air then this will have an effect.

Tension is simply a force so you add it like you did the first one.

weight=mass.gravitational field strength.

I have a feeling my assumptions could be called into question so again reference the first question and find the components and add them together if necessary.

**3)** Maximum power. Energy used per time unit, when it is at the highest?

Almost a trick question. Constant force (constant acceleration+constant friction) = constant power.

To get time I say use the equation

get a using

v^2= u^2 +2as

use the newly found a to get t via the quadratic formula (remember to make it equal 0) (u aka b in the standard quadratic = 0 which is nice). If you are getting odd results remember s is negative.

power = energy expended/time taken