Horizontal Motion Basics in Physics

Motion is when an object changes its position with respect to its surroundings with time. If the object does not change its position with respect to its surroundings with time, it is called to be at rest. Being is rest and motion are relative and depend on reference frames. This implies that an object may be in rest in one frame of reference while in motion in another frame of reference. For example, if I am standing on ground, that is my frame of reference.  Motion of anything would be compared to reference point of ground. However, if I am in a moving Bus, then moving Bus is my reference point. Any other person in Bus will be in rest for my, while for anyone standing on ground Bus and everything within that will be in motion.

One, Two and Three Dimensional Motions

Motion can be either one dimensional or two dimensional.

• In one dimensional motion, only one out of three coordinates specifying the position of object changes. Example: object falling under gravity.
• In two dimensional motion, only two out of three coordinates specifying the position of the object change. Example: Circular motion.
• In three dimensional motion, all the three coordinates specifying the position of object change with respect to time. Example: A flying bird, kite or aeroplane.

Distance and Displacement

Distance refers to the actual path traversed by an object. Distance is a scalar quantity and it can be never zero or negative. Distance is measured by meter. Displacement is the shortest distance between initial and final positions of any object during motion. Displacement is a vector quantity and can be either positive or negative or zero. Displacement is also measured in meter.

Can displacement be greater than distance?

Kindly note that magnitude of displacement can NEVER be greater than distance. This is because displacement is the shortest route connecting two positions of the particle.

Speed

Speed refers to the rate of change of position of the object in any direction with respect to time.

Speed (v) = Distance travelled (s) / Time taken (t)

The unit of speed is meter / second and it’s a scalar quantity. If the object covers equal distance in equal intervals of time, it would be uniform speed. If the object covers unequal distances in equal intervals of time, it is called non-uniform speed.

Average Speed

Average speed is the total distanced travelled divided by total time taken. When an object moves in a straight line at a steady speed, we can calculate its average speed if you know how far it travels and how long it takes. The below equation shows the relationship between average speed, distance moved and time taken:

where average speed is measured in metres per second, m/s; distance moved is measured in metres, m; and time taken is measured in seconds, s

For example, a car travels 300 m in 20 s. Its average speed is: 300 ÷ 20 = 15 m/s

Velocity

Velocity is the rate of change of displacement of an object in particular direction. Thus, Velocity is Displacement / time taken. The unit of velocity is also meter per second. However, unlike speed, velocity is a vector quantity both in magnitude and direction. Thus, velocity of an object can be positive or negative or zero.

If an object undergoes equal displacements in equal intervals of time, it would be called uniform velocity; while if it undergoes unequal displacements in equal intervals of time, it would be called non-uniform velocity. Relative velocity is the time rate of change of relative position of one object with respect to another object. The average velocity is ratio of total displacement to total time taken.

Acceleration

The rate of change in velocity per unit of time is called acceleration.

The units for acceleration are commonly written as m/s/s or m/s². The equation for acceleration can also be represented as:

a=(v-u)/t

where a is acceleration in m/s^2; v is final velocity in m/s; u is initial velocity in m/s and t is time in s

For example, a car accelerates in 5 s from 25 m/s to 3 5m/s. Its velocity changes by 35 – 25 = 10 m/s. Therefore its acceleration is 10 ÷ 5 = 2 m/s²

Deceleration / Retardation / Negative Acceleration

Deceleration, or negative acceleration, is observed when an object slows down. The units are the same as for acceleration but the number has a negative symbol before it. For example, the car slowed down at -1 m/s². For example, a car decelerates in 5 s from 35 m/s to 25 m/s. Its velocity changes by 25 – 35 = -10 m/s. Therefore its acceleration is -10 ÷ 5 = -2 m/s²

Acceleration is also a vector quantity and can be positive, negative or zero. Positive acceleration means velocity is increasing with time, zero acceleration means velocity is uniform while negative acceleration means velocity is decreasing with time. Negative acceleration is also known as retardation.

Various Graphs

Time-Displacement Graphs

In the above graphics, first graph from left is of a stationary body because there is no change in displacement with time. Second graph denotes constant velocity because equal distance is being covered in equal time intervals. Third graph is of constant acceleration because more distance is being covered as time lapses. Fourth graph is constant retardation because less distance is being covered as time lapses.

Time-Velocity Graphs

Time Acceleration Graphs

Important Basic Equations

If a body starts with velocity (u) and after time t its velocity changes to (v), if the uniform acceleration is a and the distance travelled in time t in s, then following would be the equations of uniformly accelerated motion.

Formula to get final velocity:

v = u + at

Formula to get distance covered:

s = ut + 1/2 at²

Relation between v, u, a and s

v² = u² + 2as

Distance travelled in nth second.

S_n = u + a / 2(2n – 1)

If a body moves with uniform acceleration and velocity changes from u to v in a time interval, then the velocity at the midpoint of its path:

√u² + v² / 2

Example:

A is running after a bus. The bus is travelling at an average speed of 5 m/s. The man runs 25 m in 6 s. Does he catch the bus?

Answer: No. The man’s average speed is 25 ÷ 6 = 4.2 m/s. So he will not catch a bus moving at 5 m/s.

Identify if the below statement is true or false

Two persons sitting face-to-face at the two ends of a railway compartment running at a constant acceleration toss a ball to each other with the same muzzle velocity and at the same inclination to the horizontal. The time intervals for the toss are equal in both directions.

Answer:

This is a false statement. The horizontal component of the velocity of the two balls will be equal but opposite, hence one of the ball will get accelerated while the other retarded with respect to the train, so their times of flight will be different.