1. PHYSICS IB2
Exercise Sheet 1
Derivations
Consider a particle that moves in a straight line. Its initial position is x0 ; this means that it is
located at a distance x0 from a point O that we call the origin of coordinates. By convention, if
x0 > 0 the particle is located to the right of O; and if x0 < 0 it is located to the left of O.
If the particle then moves to a point located at the position x the displacement is, by definition
∆x = x − x0 .
If its displacement is the same in equal amounts of time, we say that the particle moves uniformly.
In such case, let t be the time it takes to travel from x0 to x, then its velocity:
∆x
v=
t
is always the same. In other words, it is constant. For a body moving uniformly:
1. Prove that x = x0 + vt
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2. 2. Graph position versus time and note that the plot is a straight line. Find the intercepts with
the x and t axes. How can we find the velocity from the graph?
3. Draw the velocity-time graph and explain how to find the displacement from this graph.
Review problems
1. Object A starts from the origin with a velocity 3 m/s and object B starts from the same
place with velocity 5 m/s, 6 seconds later. When will B catch up with A? What are A and
B’s displacements in that moment?
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3. 2. An object moving in a straight line according to the velocity-time graph shown in the figure
has an initial displacement of 8 m.
(a) What is the displacement after 8 seconds?
(b) What is the displacement after 12 seconds?
(c) What is the average speed and the average velocity for this motion?
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4. 3. Find the velocity of the object whose displacement-time graphs is shown. Find also the
displacement.
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5. Problems: The Law of Gravitation
1. Stars A and B have the same mass and the radius of star A is 9 times larger than the radius
of star B. Calculate the ratio of the gravitational field strength on star A to that on star B.
2. The mass of the moon is about 81 times less than that of the Earth. At what fraction of
the distance from the Earth to the moon is the gravitational field strength zero? (Take into
account the Earth and the moon only).
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6. 3. Find the acceleration due to gravity at a height of 300 km from the surface of the Earth.
4. Hard Problem. Two stars of equal mass M orbit a common centre in a circle. The stars
are initially opposite to each other . The radius of the orbit of each star is R. Assume each
star has a mass of 3 × 1030 kg and the initial separation of the stars is 2 × 109 m.
(a) State the magnitude of each force in terms of M, R and G.
(b) Deduce that the perios of revolution of each star is given by the expression
16π 2 R3
T2 = .
GM
(c) Evaluate the period numerically.
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