Describing Motion Around Us

Chapter 1

Chapter

? Think It Over

· How much distance should we maintain from the truck ahead to avoid a collision if it suddenly applies the brakes?

· Does this distance depend upon the speed with which we are moving?

Describing Motion Around Us

4

Everything in nature is in motion, from massive astronomical objects to subatomic particles. And what a variety in motion we have in nature -flitting butterflies, slithering snakes, hopping hares, galloping horses, tendrils of climbers twinning around a support, closing of flytraps, dancing dust particles in a sunbeam, smoke particles moving in air, rising and falling of ocean tides, and gathering clouds!

Isn't motion in nature wonderful? But how do we study the wide variety of complex motions around us? As you have read in the first chapter, to explore a complex phenomenon, scientists first study it in its idealised simplified forms. Such types of motion are linear, circular, and oscillatory about which you learnt in earlier grades. In this chapter, you will learn more about Grade 6 Curiosity Chapter 5 linear motion (motion in a straight line) and uniform circular motion.

Earlier, you learnt about some physical quantities, such as distance, time and speed. Now, you will learn about some more physical quantities, such as displacement, average velocity and average acceleration. You will also learn to describe motion not only in words, but also with numbers, equations and graphs.

4.1 Motion in a Straight Line

You have learnt that when an object moves in a straight line, its motion is called linear motion. It can also be called motion in a straight line. It is the simplest kind of motion. Have you noticed it around you, such as children in a swimming race, a vertically falling ball, a car moving along a straight stretch of a highway or a train moving on a straight track (Fig. 4.1)?

Fig. 4.1: Objects in a straight line motion

To discuss about the motion of an object, you first need to describe its position at various instants of time.

4.1.1 Describing position

How do we describe the position of an object? For that, as you learnt earlier, we first need to specify a fixed point as the reference point. The distance and direction of the object with respect to the reference point, at any instant of time, describes the position of the object at that instant of time. Note that apart from the distance, we also specify the direction from the reference point in which the object is located to describe its position. And when do we say that an object is in motion? If the position of the object with respect to the reference point changes with time, the object is said to be in motion. On the other hand, the object is said to be at rest if its position with respect to the reference point does not change with time.

Fig. 4.2: An athlete running on a straight track

Note

An instant of time and a time interval are not the same thing. An instant of time is a single reading of clock at a given point of time. Whereas, a time interval is the time duration between two instants of time, i.e., between two readings of a clock.

Ready to Go Beyond

Physical quantities which can be specified by just their numerical value are called scalars. Physical quantities which require specifying both the direction and magnitude are called vectors. You will learn about these Next Level <LATEX>\mathrm { U p }</LATEX> in higher grades.

Let us take the example of an athlete running on a straight track (Fig. 4.2).

To describe the position of the athlete, let us take her starting point as the reference point. As shown in Fig. 4.3, let us make a straight line with distances marked on it and mark the reference point on it as the origin 'O'. The athlete starts running from O, and her positions at two instants of time are marked by points <LATEX>B</LATEX> and A.

Fig. 4.3: Reference point and positions of the athlete at different instants of time on a straight line

To describe the position of an object, we also need to specify its direction. For the object moving in a straight line, the object can move only in one of the two directions - forward and backward. Thus, the direction is represented by plus <LATEX>\left( + \right)</LATEX> and minus (-) signs as shown in Fig. 4.3. Positions to the right of the reference point O are generally taken as positive, and to the left of O as negative (Fig. 4.3).

4.1.2 Distance travelled and displacement

Suppose an athlete starts running from point <LATEX>O</LATEX> at time <LATEX>t = 0 \quad s ,</LATEX> reaches point <LATEX>B</LATEX> at <LATEX>t = 4 \quad s ,</LATEX> then reaches point <LATEX>A</LATEX> at <LATEX>t = 1 0 \quad s ,</LATEX> then runs back along the same path till point <LATEX>B</LATEX> reaching there at <LATEX>t = 1 6 \quad s</LATEX> (Fig. 4.4). How much is the total distance travelled by the athlete between the starting and stopping positions? The total distance travelled is <LATEX>O A + A B = 1 0 0 \quad m + 6 0 \quad m = 1 6 0 \quad m .</LATEX>

0 m

Fig. 4.4: Reference point and positions of athlete at different instants of time

Let us now think about the distance between the starting and the stopping positions of the athlete. It is <LATEX>O B = 4 0 \quad m ,</LATEX> which is different from the total distance travelled by the athlete. So, let us now define another quantity - displacement.

Displacement is the net change in the position of an object between the two given instants of time. A complete description of physical quantities like displacement requires specifying both a direction and its numerical value (with units). The numerical value (with units) of such a physical quantity is called its magnitude. The magnitude of displacement is the distance between the object's positions at the two instants. The direction of displacement is specified from the position at the first instant towards the position at the second instant. To describe the total distance travelled,

Note only the numerical value (with units) is required, not the direction of motion. The SI unit for both is the metre (m).

For motion in a straight line, the total distance travelled and the magnitude of displacement are equal if the object moves without turning back, i.e., if it moves in one direction.

For example, in Fig. 4.4, between t = 0 s and t = 16 s, the total distance travelled by the athlete is 160 m, but her displacement is 40 m in the positive direction. We find that between these two instants, the total distance travelled and the magnitude of displacement are not equal. Can these quantities ever be equal?

Activity 4.1: Let us analyse

1. As shown in Fig. 4.5, a ball is thrown vertically upwards from O. It moves up straight till B and then falls back to O. Can this be considered a motion in a straight line?

2. For this motion, fill up the values in Table 4.1.

Table 4.1: Distance travelled and displacement of the ball

S. No.

Fig. 4.5: A ball in vertical motion (two separate lines are shown only for clarity; in reality, the object goes up and falls back in the same straight line)

Pause and Ponder

1. In the example of an athlete running back and forth on a straight track (Fig. 4.4), when will the displacement of the athlete be zero? What will be the total distance travelled in that case?

2. Fuel used up in a vehicle depends on which of the following? Justify your answer.

(i) Total distance travelled

(ii) Displacement

3. A ball rolls down an inclined track as shown in Fig. 4.6. Is its motion, a straight A B D line motion? Assuming the starting point C of the ball (O) to be the origin, can its Fig. 4.6: A ball rolling down an inclined track motion from O to D be depicted using a horizontal line as shown in Fig. 4.3? Are the values of total distance travelled and magnitude of displacement from O equal or different at positions A, B, C and D?

Motion, i.e., a change in the position of an object, can be described in terms of the total distance travelled by the object and its displacement. But how can you describe how fast or slow an object is moving?

4.1.3 Average speed and average velocity

You have learnt about average speed in an earlier grade. It tells us how fast or slow an object moves. The average speed of an object is the total distance travelled divided by the time interval during which this distance is covered. Thus,

average speed = total distance travelled time interval (4.1)

Since distance travelled has no direction (but only a numerical value), the average speed, which is calculated from distance travelled, also has no direction but only a numerical value.

If an object moving in a straight line travels equal distances in equal intervals of time (for all possible choices of time intervals), it is said to be in uniform motion in a straight line. In this case, the object moves at a constant speed. On the other hand, if the object travels unequal distances in equal intervals of time, then it is in non-uniform motion in a straight line. In this case, the object moves with increasing speed or decreasing speed, or a combination of both. If the distances travelled in the successive intervals of times are increasing, its speed is increasing.