Chapter 13

Motion and Time

Motion and Time are among the most popular concepts in Physics. The concept of motion and rest only applies to objects that have mass. Motion and time are two interdependent quantities that are written out as mathematical numbers in detail. The SI unit of speed and velocity is metres per second. These concepts are very useful in day to day applications. Some of the sub-topics taught in this chapter are mentioned below.

What is Motion?

Motion is a fundamental concept used in physics. It is determined as a change in the position of an object to its surroundings in a given interval of time. This concept only applies to objects having mass. The motion of the object can be described in terms of distance, displacement, speed, velocity, time and acceleration. 

Furthermore, different types of motion depend on the force acting on the body. Some of the types are translational, rotational, linear, periodic and others.

What is the Reference point?

A reference point is an important concept in understanding the motion of the object. A reference point can be defined as the stationary point that determines the motion of the object. Consider a man inside a moving train. We can see the man travelling in the direction of the train if we look at him from outside the train. As a result, the man appears to be moving to the outside observer. But what if we look at him through the eyes of the man seated just in front of him? Then he sees the man at rest- like himself. Hence, in Physics motion concepts, the reference point is very important.

 

Speed 

Velocity

Speed is defined as a rate at which a body covers a certain distance.

Velocity is defined as the rate at which a body changes position in a certain direction.

It is a Scalar Quantity.

It is a Vector Quantity.

Speed can never be negative or zero.

Velocity can be positive, negative or zero.

Even if the object changes direction, the average speed will continue to count.

Because the object's velocity changes as the direction changes, the object must only go in one direction.

Speed may or may not be equal to the velocity.

An object may possess different velocities but has the same speed.

Unit of Speed is m/s.

Units of Velocity is m/s.

 

Types of Speed

There are 3 types of speed. These are

  • Uniform Speed - When an object travels the same distance in the same amount of time, it is said to be moving at a uniform speed. For example, a car driving on a straight road will travel at a uniform speed.
  • Non-Uniform speed - When an object traverses a varying distance at equal intervals of time, it is said to be at variable speed. For example, the speed of a bike is non-uniform on busy roads.

Average Speed - Average speed is defined as the consistent speed determined by the ratio of the total distance travelled by an object to the total time spent by the object.

Time is a scalar quantity that is measured in seconds, which is the SI unit of time. We have several conversion factors, which are listed below:

1 minute = 60 seconds

1 hour = 60 minutes.

1 hour = 3600 seconds

Distance Time Graph

A distance-time graph depicts the distance travelled by an object in a given amount of time. It's a straight line graph that depicts distance versus time findings. The Y-axis represents distance. Furthermore, the x-axis represents time. The distance-time graph is useful for the following findings

  • The motion is uniform if the distance-time graph is a straight line.
  • If a person's distance-time graph is provided, the slope of the graph can be used to compute their speed.
  • The slope of a straight-line graph remains constant regardless of the interval used. This means that the speed of an object moving at a constant rate remains constant.

How to make a Distance Time Graph

  • Divide the graph sheet into four quadrants with equal space between them. The X-axis and the Y-axis are the two axes utilised for intersection and division.
  • One axis should represent distance, while the other should reflect time.
  • Mark the time and distance values on the graph based on the data sets.
  • To get your needed distance-time graph, combine these points with their nearby points.
  • It is a uniform motion if the data sets on the graph display a straight line. It's a non-uniform motion otherwise. Motion and time are inextricably linked.

Periodic motion can be simply defined as the motion which occurs at a fixed interval of time. Periodic motion is depicted by the movement of the swing and the pendulum. They tend to oscillate between two extremes. As the car moves between an extreme fixed position at regular time intervals, a vehicle driving uniformly between point A and point B in a straight path is also considered periodic motion. The periodic motion will continue indefinitely until it is affected by other external factors.

Question:
When the clock reads 08:30 AM, the odometer of a car reads 57321.0 kilometres. What is the distance travelled by car if the odometer reading has changed to 57336.0 km at 08:50 AM? Calculate the car's speed in kilometres per minute at this time. Also, express the speed in kilometres per hour (km/h).

Solution: 

The odometer's initial reading was 57321.0 miles.
Last reading of the odometer - 57336.0 miles

The odometer's final reading minus the odometer's initial reading equals the distance travelled by car.

15 km = 57336.0 – 57321.0

The vehicle starts at 8:30 a.m. and stops at 8:50 p.m.

As a result, the time taken by car is 20 minutes.

we know that, 

Speed = Distance/time = 15/20 = 0.75 km/min
Now, 20 min = 1/60 * 20 = ⅓ hrs

Speed = Distance covered/ Time taken
= 15/(1/3)
= 45 km/h

Question:
Salma rides her bicycle 15 minutes from her house to her school. Calculate the distance between her home and the school if the bicycle travels at a speed of 2 m/s.

Solution: 

Time taken by Salma to reach school by bicycle - 15 mins = 15*60 = 900 secs

Speed of Salma’ bicycle = 2 m/s

Speed = Distance/Time
Therefore, Distance = Speed x time

= 2 * 900 = 1800 m
= 1800 * 1/1000 = 1.8 km

Question:
It takes 32 seconds for a simple pendulum to complete 20 oscillations. What is the pendulum's period?

Solution:

Number of Oscillations = 20
Total time taken to complete 20 oscillations = 32 sec

Time period = Total Time taken/ Number of oscillations

= 32/20 = 1.6 secs

Which of the following are not correct?

(i) Kilometers are used to measure the distance between two cities.

(ii) The speed of a train is expressed in m/h.

(iii) The basic unit of time is second.

(iv) The time period of a given pendulum is constant.

(v) Every object moves at a constant speed.

Solution:

Incorrect statements are:

(v) Every object moves at a constant speed.

(ii) The speed of a train is expressed in m/h.

(iv) The time period of a given pendulum is constant.

Question:
For 15 minutes, a car travels at 40 kilometres per hour, then at 60 kilometres per hour for the next 15 minutes. The car has travelled a total distance of

(i) 100 km (ii) 25 km (iii) 15 km (iv) 10 km

Solution:

Speed of the car = 40 km/hr

Time taken = 15 min = 15/60 = 0.25 h

Speed = Distance/time

Distance covered d1 = speed x time taken

= 40 x 0.25 = 10 kms

Now, Speed of Car = 60 km/hr

Speed = Distance/time

Distance covered d2 = speed x time taken

= 60 x 0.25= 15 kms

Total distance covered by the car = d1 + d2

= 10 + 15

= 25 kms

Therefore the option is (ii) 25 kms

Question:
Which of the following relations is correct?

(i) Speed = Distance × Time

(ii) Speed = 1/Distance x Time 

(iii) Speed = Time/Distance

(iv) Speed = Distance/Time

Solution:

Answer is (iv) Speed = Distance/Time

The concepts of motion and time are very useful in understanding different physics concepts like kinematics and mechanics. Its applications can be easily drawn from daily life examples. Furthermore, Speed and Velocity are concepts that are used to describe motion.

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