Question

What was the velocity of the student at $9$ seconds?
Distance $/m$ $01234566630$
Time $/s$ $012345678910$

Answer 1

The data given should be used and the correct value for distance for the given time should be found out. The concept of velocity with respect to the distance and time is applied. The formula for velocity in terms of distance and time must be applied, that is, the speed-distance formula must be applied in order to find the velocity at a given time.

Formula used:
The velocity or the speed of a moving object is given by the formula:
$\text{speed} = \dfrac{d}{t}$
Where, $d$ denotes the distance and $t$ denotes the total time taken.

Complete step by step answer:
The above problem revolves around the concept of velocity and its relation with quantities like distance and time. In-order to find these quantities we must first know their concept. We consider the body exhibiting some motion to be moving in a straight line motion and hence the velocity and speed quantities can be thought of to be the same.

Velocity is always calculated when an object is in motion, that is, when an object is said to be moving with respect to another object which is stationary and viewing the object in motion.The body in motion will cover some amount of distance within a time period or a time interval and hence the three quantities relate to each other.

The average speed is defined as the total distance travelled by the object divided by the total time taken to cover that distance. The average speed is always calculated for an object moving with variable speed. The term average refers to the net or the total of the quantity that is considered since the body may move with variable motion so the total distance over that particular time interval is calculated. The equation for the average speed is given by the formula:
$\text{speed} = \dfrac{d}{t}$ --------($1$)

The question gives a series of data which indicates a set of distances and the corresponding time taken to cover each of these distances. The distances are recorded in a continuous manner and the time taken varies linearly. This means that the distance covered by a body said to be in constant motion per second is recorded and this is the data that is given. The distances at each instant of time is given which means that the instantaneous values of distances values have been given.

The term instantaneous here, refers to the value of distance at that particular instant of time. We have been asked to find the velocity of the object at $9$ seconds.Here, the velocity is asked but the formula to be used, that is, equation ($1$) gives the formula for speed. We are considering the speed and velocity quantities to be the same as their concepts are said to be the same.

Let us now extract the data given in the question. The distances are recorded for each second, we must first find out the distance covered in $9$ seconds in order to determine the velocity at $9$ seconds. We must match and find the corresponding distance at $9$ seconds from the data that is given. As we can see in the given series of distances and time we can clearly conclude that for $0$ seconds, $0$ meters are covered and for $1$ second, $1$ meter is covered and so on. Similarly if we look into the given data we can see that for $9$ seconds, the distance covered is $3\;m$.

Given, $d = 3\;m$ and $t = 9s$. We now substitute these values into equation ($1$) in order to determine the velocity at $9$ seconds. Hence we get:
$\Rightarrow velocity = \dfrac{d}{t}$
$\Rightarrow \text{velocity} = \dfrac{3}{9}$
On further simplification we get:
$\Rightarrow \text{velocity} = \dfrac{1}{3}$
We get a recurring value as velocity:
$\Rightarrow \text{velocity} = 0.333\;m/s$
We round off this value to approximately $2$ significant figures and hence we get:
$\therefore \text{velocity} \approx 0.33\;m/s$
The distance is given to be in meters and the time is given to be in seconds and hence the velocity will be in $m/s$ as this is the SI unit of velocity as well.

Hence, the velocity at $9$ seconds is $0.33\;m/s$.

Note: Even-though speed and velocity seem similar to each other the two quantities actually have two differing concepts and are often mistaken to be equal. This is because speed, which is a scalar quantity, depends on the distance covered and velocity which is a vector, depends on the displacement. However these quantities can be equal in certain conditions like when a body is traveling in a straight line in motion in the same direction.