Kinematics

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A stone is thrown at an initial speed of 15 m/s from the top of a 20 m high cliff, while another stone is thrown
vertically from the bottom of the cliff upwards also at a speed of 15 m/s, the free-fall acceleration is equal to
10 m/s^{2}, find:

a) After how long and at what height do the stones intersect?

b) Does the stone throw from below reach the top of the cliff?

a) After how long and at what height do the stones intersect?

b) Does the stone throw from below reach the top of the cliff?

A rocket is launched vertically from the ground at an initial speed of 200 m/s, after 10 seconds it explodes.
A ground observer located at a distance of 2000 meters, the same horizontal as the launch point, will hear the
blast noise after how long? The free-fall acceleration is 10 m/s^{2}, and the speed of sound in the
air 340 m/s.

On the Moon a stone is released at rest from a height of 20 meters, it falls under the action of the lunar free-fall
acceleration until reaching the ground with a speed *v*. Determine how high the stone should be dropped on Earth
so that it hits the ground at the same speed *v*. Free-fall acceleration on Earth
*g*_{T}=9.8 m/s^{2}, free-fall acceleration on the Moon
*g*_{L}=1.6 m/s^{2}.

The motion of a particle is described by the graph of the speed t as a function of time shown in the figure.
Find:

a) The acceleration of the particle;

b) Write the equation of the speed as a function of time;

c) What is the displacement between 3 s and 7 s.

a) The acceleration of the particle;

b) Write the equation of the speed as a function of time;

c) What is the displacement between 3 s and 7 s.

The velocity-time graph
\( v=f(t) \)
gives the motion of a body:

Find:

a) The displacement between 1 s and 9 s;

b) The average speed between 1 s and 9 s;

c) The average acceleration between 1 s and 9 s.

Find:

a) The displacement between 1 s and 9 s;

b) The average speed between 1 s and 9 s;

c) The average acceleration between 1 s and 9 s.

Solution** by area calculation**

Solution** by direct counting**

A particle starts a straight motion with an initial velocity of 1 m/s, given the graph of the acceleration as a
function of time from the start of motion, find:

a) the velocity at*t*=8 s;

b) The velocity at*t*=12 s;

c) The velocity at*t*=14 s;

d) Between, which time interval the speed decreases.

a) the velocity at

b) The velocity at

c) The velocity at

d) Between, which time interval the speed decreases.

The equation of a motion is

*S* = 21 − 10 *t* + *t*^{2}

where position*S* is measured in
meters and time *t* is measured in seconds:

a) Construct a table with values for*t* from 0 to 8 s, and from the table plott the graph of the function;

b) When does the particle pass through the origin of the coordinate system?

c) When does the particle change its direction?

where position

a) Construct a table with values for

b) When does the particle pass through the origin of the coordinate system?

c) When does the particle change its direction?

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Fisicaexe - Physics Solved Problems by Elcio Brandani Mondadori is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License .