What is Motion ?

There are two aspects of an object in motion. The first aspect is to describe the motion itself. Describing motion is studied under Kinematics. Is the body moving fast or slow? Is it moving forward or backwards? Is it moving to the left or to the right of the reference position? Knowing the position of the body describe its motion.

The second aspect of motion is to understand what causes the motion. The forces that cause the motion are studied under Dynamics. The Kinematics and Dynamics of the motion together constitute the Mechanics.

Motion is the change in position of a body. To describe the change in position, we need to know the body’s initial position and its position at a particular time.

Distance and Displacement

Let’s look at an example. In Fig 1, the initial position of the car is x_o and its position after moving for time t is x. The difference in the position coordinates of the car (x-x_o) during the time of travel (t) represents the distance traveled by the car. Since the car is moving along a straight line, (x-x_o), it also represents the displacement of the car along the +x axis. Displacement is the shortest straight-line distance between the initial and final position of the body. It is a vector quantity, and the direction is indicated with an arrow pointing from the initial to the final position of the body. 

Here the motion of the car is from left to right along +x axis, so the displacement is taken as positive (e.g. +100m). If the motion was along –x-axis (from right to left), the displacement would be indicated by a negative sign (e.g. -100 m). In such a case, the displacement along one direction is taken as positive and the opposite direction as negative.

Motion is not always along a straight line—it may be along a curved path too. Fig 2 shows a cyclist riding along a twisted curved path. The total distance is the actual length of the path covered during the ride. Displacement, on the other hand, is the shortest straight-line path length between the initial and final positions of the cyclist. 

What is the direction of displacement of the cyclist?

The arrowhead from the initial location towards the final location of the cyclist indicates the direction of displacement.

Note that along a curved path, the displacement is always lesser than the actual distance traveled. However, along a straight-line, the displacement and the distance traveled are the same.

What are the units of displacement and distance? Both have the same units—meter, kilometer, feet, miles, etc.

Speed and Velocity for Describing Motion

Consider traveling from San Francisco  by road to California, which is about 340 km. The journey by car could take about 4 hours. So, the rate at which the car moves, i.e., the velocity is 340/4 or 85 km per hour in the southward direction. This is actually the average velocity of the car. The average  value however does not tell much about the journey itself. If the path of the journey is broken into small pieces—each piece being a straight line covered in one second by the car with constant speed, then this speed is called instantaneous velocity of the car. It would represent how fast or slow the car moves in that moment and in which direction.

Lab Example of Measuring Time and Distance

Measuring time using stopwatches may lead to manual errors. Using stopwatches for measuring time always depends upon the individual’s response time to begin and stop it.

Photogates are light sensitive meters that record the time instantly, as soon as an object crosses it. It is efficient, sensitive and accurate. In the lab set up, a billiard ball is made to roll along a straight path on a perfectly smooth surface. Six photogates spaced 5 cm apart are placed along the straight line path (Fig 3).

As the ball is released, and it passes through each of the 6 photogates, time instants are recorded for every 5 cm travel of the ball on the surface by the successive photogates. The observations are repeated at least four times for accurate results.

Using these values, if a distance time graph is plotted as below, it would be a straight line indicating the uniform motion.

The straight line graph implies that the ball travels equal distances in equal time intervals. Therefore, it’s a uniform motion for the billiard ball on a perfectly smooth surface along a straight line. Note that in such circumstances the average velocity is equal to instantaneous velocity.

Speed cameras work very much like photo gates. They measure the speed of the vehicles passing by a certain section of the road or highway. A typical speed camera would take two photos—as the car moves across the start and end points of a measured section of the road. The time interval measured between the two locations will enable the calculation of speed which is equal to distance/time interval by the speed camera. Based on the technology deployed to measure the speeds of the incoming vehicles, there are different types of speed cameras: mobile systems, fixed speed cameras and average speed cameras.

Mobile speed cameras are based on radar systems. Fixed speed cameras use piezo electronic detectors (tiny wires) embedded into the road surface. The average speed cameras, mostly handheld ones, do not use lasers, beams, GPS or any other modern invention, but the good old photo camera and a little bit of math.

Ever heard of nautical miles and knots in context of distance and speed?

Yes, you would use them, if you were a sailor!

Nautical mile represents distance measured in water. 1 nautical mile is about 1.852 km or 1.15 miles of land length. Another way of defining a nautical mile is based on the Earth’s longitude and latitude coordinates. One nautical mile equals one minute of latitude. A nautical mile is based on the curved circumference of the planet Earth.

How much of Earth's length makes one nautical mile?

Cut the Earth in half at the equator. Pick up one of the halves and look at the equator as a circle. Divide the Earth circle into 360 degrees and then divide each degree into 60 minutes. A minute of arc on the curved planet surface Earth is 1 nautical mile. This unit of measurement is used by all nations for air and sea travel as a standard convention.

Knots, on the other hand, are used to measure speed by marine navigators. One knot equals one nautical mile per hour.

Practice Problems

Q1. Average speed of the body is equal to average velocity only in case the body is moving along a straight line.

1. True
2. False

Answer: True

Explanation: In the case of a body moving along a straight line, the distance travelled by the body and its displacement are equivalent in any time interval. So, in this case, the average speed of the body is always equivalent to the average velocity. Hence, option (a) is correct.

Q2. For a moving particle, distance can be negative or zero while displacement cannot be.

1. True
2. False

Answer: False

Explanation: The distance travelled by a particle cannot be negative or zero in any situation whereas, displacement can be. So, option (b) is correct.

Q3. For a body in motion, distance can never decrease with time, but displacement can.

1. True
2. False

Answer: True

Explanation: The distance travelled is a path dependent physical quantity and hence, will always increase with time. The displacement is a path independent quantity and can decrease with time whenever the body reverses its path or changes direction during its motion. So, option (1) is correct.

Q4. For a given time interval, average speed is single valued while, average velocity can have many values depending on the path followed.

1. True
2. False

Answer: False

Explanation: The average speed of the body is the magnitude of the average velocity of a body in any time interval. So, average speed cannot be single valued while average velocity is taking multiple values. Hence, option (b) is correct.

Q5. If the velocity is constant, the speed will be necessarily constant. But the converse may or may not be true.

1. True
2. False

Answer: True

Explanation: Speed of the body is the magnitude of its velocity at any instant and hence, it is always constant when the velocity of the body is constant. But the speed of the body being constant does not necessarily imply that its velocity is constant. So, option (1) is correct.

Context and Applications

The speed, distance and time relation forms the basis of study of motion. You will need these concepts in the study of Mechanics. This concept is applicable for students who are studying the following courses –

• Bachelors in Technology
• Masters in Technology
• Bachelors in Science in Physics
• Masters in Science in Physics