Kinematics

### Free Fall

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/s2, 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 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/s2, 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 gT=9.8 m/s2, free-fall acceleration on the Moon gL=1.6 m/s2.

### Graphs

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. 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.
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.
The equation of a motion is

S = 21 − 10 t + t2

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?