Alan

To check geno's results here's an alternative approach:

Acceleration:  use v² = u² + 2as where v is final velocity, u is initial velocity, a is acceleration, s is distance.

$${\mathtt{a}} = {\frac{\left({{\mathtt{45}}}^{{\mathtt{2}}}{\mathtt{\,-\,}}{{\mathtt{78}}}^{{\mathtt{2}}}\right)}{\left({\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{0.345}}\right)}} \Rightarrow {\mathtt{a}} = -{\mathtt{5\,882.608\: \!695\: \!652\: \!173\: \!913}}$$  km/hr²

So 

a = -5882.608*1000/3600² m/s² = -0.4539 m/s²

Time taken: use distance/average speed

average speed = (45 + 78)/2 km/h = 61.5 km/hr

time taken = 0.345km/61.5km/hr*3600s/hr = 20.195 seconds

Any differences from geno's results are just due to small numerical rounding errors, as his approach was perfectly ok.

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Are these links any use?

I'll have a look for some practice problems.

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Sorry Melody, in my last reply I confused part of question 1 with question 2.

As far as question 2d is concerned, if the body is travelling in a circle the velocity is changing (though the speed might not be).

2a) Any acceleration will change the velocity, so 2a) is possible.

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Another way to think of this question is as follows:

Imagine a sphere of radius, s.  The volume of this sphere is (4/3).pi.s³.

Imagine it is surrounded by a larger sphere of radius s+δs.  The volume of this sphere is (4/3).pi.(s+δs)³.

The volume of the shell between them is therefore (4/3).pi.(s+δs)³ - (4/3).pi.s³.

This shell volume is therefore: (4/3)*pi*(3.s².δs + 3.s.δs² + δs³)

Now we are going to shrink the thickness of this shell until we can ignore terms involving higher than linear powers of δs.  So an infinitesimal thickness shell will have a volume of 4.pi.s².ds  (where I've replaced δs by ds for the infinitesimal limit). Now the mass in this infinitesimally thin shell is just density*volume or

(1/s(1+s)³)*4.pi.s².ds

This is an infinitesimal mass, of course, so to get a non-infinitesimal mass we have to sum (integrate) this between one radius and another. The second radius is a non-infinitesimal distance away from the first. In this problem the question is clearly asking for the first radius to be zero and the second to be infinity. So the total mass is given by the integral shown in my first reply above.

I'm not sure that I've got any more general advice on how to approach these sort of problems, except for: do a lot of examples.  I must have done hundreds (thousands?) of these over the years!

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4) Ball rolling down hill.

A ball rolling down a hill, in the absence of any significant friction or drag, is going to speed up, so the answer will be one with speed increasing.

The acceleration will result from the component of the gravitational force tangential to the surface of the hill.  Because the slope is decreasing as we move towards the bottom of the hill, this component is decreasing (when the ball is on the flat at the bottom of the hill, the tangential component of acceleration is zero, of course).

2) d:  Constant velocity must mean zero acceleration, so one cannot have constant velocity with changing (i.e. non-zero) acceleration.

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Yes, your answer is correct.

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No, on second thoughts, I agree with your answer (I looked at this too quickly!)

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Edited.  

See further reply below.

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That's correct!

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