*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)=t*^{2}**,**

*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?

*Answer*:

**,**

*x(t)=t*^{2}−5**,**

*y(t)=0***.**

*z(t)=0**Problem 2*

An object is falling down along the Z-axis from a point

**)**

*0, 0, 25*

*x(t) = 0*

*y(t) = 0*

*z(t) = 25 − t²/4*How long will it take for this object to hit the ground?

*Answer*:

*T = 10**Problem 3*

An object is falling down along the Z-axis from a point

**)**

*0, 0, 25*

*x(t) = 0*

*y(t) = 0*

*z(t) = 25 − t²/4*What is the object's speed when it hits the ground?

*Answer*:

*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?

*Answer*:

*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?

*Answer*:

*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?

*Answer*:

*840 km; 84 km/hr*
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