Motion

When an object changes its position with time, the object is said in the motion. And when an object does not change its position with time, the object is said in the rest.

To understand motion three things are necessary. These things are A reference point, time and object.

This is because we observe an object in motion with the lapse of time and with respect to a reference point.

Example: Often we say that our school or a shop is 2 km or four km from our house. Here, our house is taken as reference point, from which distance is considered.

Types of Motion:

Motion is of many types, such as motion along a straight line, motion along a circular path, zig-jag or erratic motion, controlled motion, uncontrolled motion, Uniform motion, Non-uniform motion, etc.

Motion Along A Straight Line

When an object changes its position with time along a straight line, this is called the Motion along a Straight line.

Example: If a cyclist goes along a straight road, the motion of cyclist is called along a straight line.

If you run along the border line of one side of a football field, your motion is called along a straight line.

Distance and Displacement

Distance

The total length of path is called the DISTANCE. Distance is a physical quantity and has magnitude only.

Displacement

The distance between initial position and final position of an object is called DISPLACEMENT. Displacement is a physical quantity and has magnitude and direction both.

Example:

Case: I

Let an object starts moving from a point A and reaches to B in the given time.

Thus, here distance covered by object = 70 km

Here displacement, i.e. change in position of the given object is also equal to 70 km west. That is from point A to B.

Case : II

Let an object starts moving from point A and reaches to B and return to C and stops.

Thus, distance = total length of path

= Distance from A to B + Distance from B to C

= 70 km + 40 km = 110 km

Thus, distance covered by the object = 110 km

And, Displacement = distance from initial position A to the distance of final position C.

Or, Displacement = Distance between initial position A and C

Or, Displacement = 30 km

Thus, here, distance covered by the object = 110 km

And displacement of the object = 30 km west

Thus, distance is the length of path covered by an object in the given time and displacement is the change of position by the object in the given time. Distance and displacement both are physical quantities. Distance has only magnitude while displacement has magnitude and direction both.

Thus, two different physical quantities – the distance and the displacement are used to describe the overall motion of an object and to locate its final position with reference to its initial position at a given time.

Example Problem (1): A cyclist starts from point A and reaches to a point D through points B and C as given in the figure. Then find the distance covered and displacement of cyclist.

Solution:

Here, As per figure given in question Distance from A to B = 50 m

Distance from B to C = 60 m

And, Distance from C to D = 50 m

And, Distance from A to D = 60 m

Now, total distance covered by cyclist = Distance from A to B + Distance from B to C + Distance from C to D

= 50 m + 60 m + 50 m

= 160 m

Thus, distance covered by cyclist = 160 m

Since cyclist reaches to point D, thus displacement

= distance from initial point A to final point D

= 60 meter

Thus, distance = 160 m And displacement = 60 m Answer

Example Problem (2): A person starts from a point A and goes 3 meter straight towards east direction and from there he goes 4 meter straight towards north direction and stops. Find the distance covered and displacement of the person.

Solution:

Let, person Starts from point A and goes 3 m and reaches to B i.e. in east direction.

From there, i.e. from point B he goes 4 m towards north direction, i.e. from B to C

Distance covered =?

Displacement =?

Now, distance covered by him = Distance from A to B + Distance from B to C

= 3 m + 4 m = 7 m

And displacement = distance from initial point A to point C = AC

Now, according to figure, `/_ B =90^o`

Thus, AB = base and BC = height and AC = hypotenuse

We know from Pythagoras Theorem

`AC^2 = AB^2+ BC^2`

`=>AC^2 = (3\ m)^2+(4\ m)^2`

`=>AC^2 = 9\  m^2 + 16\  m^2`

`=>AC^2 = 25\  m^2`

`=>AC = sqrt(25\  m^2)`

`=>AC = 5\  m`

Thus, distance covered = 7 m and displacement = 5 m Answer

Uniform Motion

When an object covers equal distance in equal interval of time, the motion of the object is called UNIFORM MOTION.

Example:

(a) Suppose a car covers 1 km of distance in first 10 minute and again covers 1 km in second 10 minute and again cover 1 km of distance in third 10 minute.

In other words, if that car covers 1 km of distance in every 10 minute of time, the motion of the car is called UNIFORM MOTION.

(b) Minute hand of a clock complete one round in every 1 hour. On the other hand hour hand of a clock completes one round in every 12 hour. And minute hand of a clock completes one round in every one minute.

Here, since hands of a clock cover same distance in equal interval of time, thus, motion of hands of clock is called UNIFORM MOTION.

Non–Uniform Motion

When an object does not cover equal distance in equal interval of time, then the motion of the object is called NON–UNIFORM MOTION.

Example:

(a) A car travel more distance while running to a free road, i.e. without any traffic and covers less distance on road with traffic, hence, in this condition the motion of the car is called NON–UNIFORM MOTION.

(b) A fly covers unequal distance in equal distance of time, thus motion of a fly is called NON–UNIFORM MOTION.

Measuring the Rate of Motion

Speed

Rate of Motion is called speed. Rate of motion or speed is the distance travelled by an object in unit time. In other words, distance travelled or covered by an object in unit time is called SPEED or RATE OF MOTION.

Thus, speed of an object is calculated by dividing distance by time.

Thus, `text{Speed}=(text{Distance})/(text{Time})`

Speed is a physical quantity.

The SI unit of speed is meter per second.

The SI unit of speed or rate of motion is represented by the symbol `m//s` or `m s^(-1)`

Here distance is measured in meter (m) and time is measured in second (s).

The other unit of speed is centimeter per second or cm/s or `cm s^(-1)`.

Here distance is taken in centimeter and time is taken in second.

And another unit of speed is kilometer per hour or km/h or `km h^(-1)`.

Here distance is taken in kilometer and time is taken in second.

In cars, buses, etc. speed is measured in km/h in India.

Average Speed

The speed of the object is need not to be constant because in most cases objects will be in non–uniform motion. Thus rate of motion of such object is described in the term of Average Speed.

Average Speed of an object is obtained by dividing the total distance covered by the total time taken.

Thus, `text{Average speed} = (text{Total distance travelled})/(text{Total time taken})`

The distance is generally denoted by `s`

The time is generally denoted by `t`

And speed is denote by `v`

Thus,

Speed `v = s/t`

Example Problem (1) : If a car travels a distance of 200 meter in 5 second, then find its speed.

Solution:

Here given, distance (`s`) = 200 meter

Time (`t`) = 5 second

∴ speed (`v`) =?

We know that, `v=s/t`

`:. v = (200\  m)/(5\  s)`

`= 40\  m\  s^(-1)`

Thus, speed (`v`) = `40\  m\  s^(-1)` Answer

Example Problem (2) : If a bus reaches from Allahabad to Varanasi in 3 hours. If the distance from Allahabad to Varanasi is 150 km, then find the speed of bus.

Solution:

Given, Distance (`s`) = 150 km

Time (`t`) = 3 hours

∴ Speed (`v`) =?

We know that, `v=s/t`

`:. v = (150\  km)/(3\  text{hour})`

`= 50\  km//  hour`

Example Problem (3): If a train covers 150 km in 4 hours and 300 km in 5 hours, then find its average speed.

Solution:

Given, Total distance (`s`) = 150 km + 300 km = 450 km

Total time taken (`t`) = 4 hours + 5 hours = 9 hours

Thus, Average Speed (`v`) =?

`:. v = (450\ km)/(9\  text{hour})`

`= 50\  km\  hour^(-1)`

Thus, Average speed (`v`) `= 50\  km\  hour^(-1)` Answer