1)a cyclist travels ¾ of a circular track from a to b as shown in figure. the radius of the circular track is 400 m. calculate the displacement and distance travelled by the cyclist.

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2)two objects having their masses 3: 5 are acted upon by two forces. the forces are in the ration of 5: 3. find the ration in their accelerations.

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3) a man pushes a box of mass 50 kg with a force of 80 n. what will be the acceleration of the box due to the force? what would be the acceleration if the mass were doubled?

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4) how does the force of gravitation between two objects change when the distance between them is reduced to half.

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5) explain what happens to the force between two objects if:
a) the mass of one object is doubled?
b) the distance between the object is tripled.

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6)how will the equations of motion for an object moving with a uniform velocity change?

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7)the force of attraction between two bodies is 20n. calculate the force between them when mass of each body as well as the distance between them are halved.

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1).  Distance is the length of the path he traveled.  That's 3/4 of the circle.

Displacement is the length between where he started and where he ended.
That's 1/4 of the circle.

The circumference of a circle is  (2 pi) · (the circle's radius) .

2).  Force = (mass)·(acceleration)            F = M·A
This is a very important formula.  You should memorize it. 
Whenever you see a problem that has force, mass, and
acceleration in it, this is the formula you need.

If you need to find acceleration (like in this problem),
divide each side by (mass), and then you have
           
                        Acceleration = (force) divided by (mass) .

First object:  Mass=3,  Force=5.  Acceleration= 5/3 .

Second object:  Mass=5,  Force=3.  Acceleration= 3/5 . 

The question is asking for the ratio of these forces.

3).  Guess what !        F = M · A .

Divide each side by Mass, and then you have

                 Acceleration = (force) divided by (mass)

                                       =  (80 N)  /  (50 kg)  =  ?

If the mass were doubled, it would be

                                           (80 N)  /  (100 kg)  =  ?

4).  The force of gravity changes opposite to the distance between
the objects.  That's why the Earth pulls on us harder than Jupiter does.
The farther apart things are, the WEAKER gravity pulls them together.

How fast does the gravity force decrease ?
It decreases with the SQUARE of the distance.
That means . . .
-- If the distance changes to 3 times as far, the force becomes 1/3² = 1/9 .
-- If the distance changes to 2 times as far, the force becomes 1/2² = 1/4 .
-- If the distance changes to 1/3 as far, the force becomes (3²) = 9 .
-- If the distance changes to 1/2 as far, the force becomes (2²) =  ?

5).  A). The force of gravity increases as much as the PRODUCT of
the masses increases.
If one mass is B and the other mass is D, then the force calculation
has 'B·D' in it.  If one of the masses doubles, then the calculation
has '2·B·D' in it.  How much did the original force change ?

5). B).  This was all covered in the discussion of #4).

6). 'Uniform velocity' means the object is moving in a straight line
with a constant speed.  Its speed is not changing, and its direction
isn't changing either.
If a little tiny physicist is riding inside that object, there's NO TEST
he can do that can show him that he's moving.  He has all of the SAME
laws of motion that any other physicist has, who's moving in any other
direction with any other constant speed.

7).  Their masses are 'B' and 'D'.   The original product is 'BD'.
When each mass is cut in half, they'll become B/2 and D/2.
Their product will become  BD/4 .
That change alone will change the force to 1/4 of what it was originally.

If the distance between them is cut in half, then the force
changes to (2²) = 4 times what it was originally.

So the combined effect of all these changes at the same time
is that the new force is exactly equal to the original force.