## Friday, April 20, 2018

### Unizor - Physics - Mechanics - Kinematics - Problems

Notes to a video lecture on http://www.unizor.com

Problems on Kinematics

In these and most other cases the units of distance are a meters and derived from it units (like kilometers, millimeters etc.), unit of time is a second or an hour, unless otherwise explicitly specified

Problem 1

Assume a motion along a straight line coinciding with X-axis and represented by a position functions

x(t)=t2, y(t)=0, z(t)=0.

What form the position functions will take in a new coordinate system
with the new origin at old coordinates (5,0,0) and all new axes parallel
and similarly directed to old axes?

x(t)=t2−5, y(t)=0, z(t)=0.

Problem 2

An object is falling down along the Z-axis from a point (0, 0, 25) according to the following coordinate functions:
x(t) = 0

y(t) = 0

z(t) = 25 − t²/4

How long will it take for this object to hit the ground?

T = 10

Problem 3

An object is falling down along the Z-axis from a point (0, 0, 25) according to the following coordinate functions:
x(t) = 0

y(t) = 0

z(t) = 25 − t²/4

What is the object's speed when it hits the ground?

V = −5 m/sec

Problem 4
A projectile is launched from the ground within a vertical XZ-plane at
an angle to horizon. It moves according to the following coordinate
functions:

x(t) = 2·t

y(t) = 0

z(t) = 10·t−t²

How far will it fly until landing to the ground?

20 m

Problem 5

A train goes from point A to point B. The distance between these points
is 720 km. The first half of this distance a train moves with an average
speed of 60 km/hr. The second half of the distance it moves with an
average speed of 90 km/hr.

What is the average speed of this train on its way from A to B in km/hr and m/sec?

72 km/hr = 20 m/sec

Problem 6

A train goes from point A to point B, and the entire travel time is 10
hours. The first and the last time intervals of one hour a train
accelerates and decelerates and moves with an average speed of 60 km/hr.
The rest of the entire time (between acceleration and deceleration) it
moves with an average speed of 90 km/hr.

What is the distance from A to B? What is the average speed of a train on its way from A to B in km/hr?