Question

A particle moves in the direction of east for $2\,s$ with velocity of $14\,m/s$. Then it moves towards north for $8\,s$ with a velocity of $5\,m/s$. The average velocity of the particle is (in m/s)

A. 1

B. 5

C. 7

D. 10

Answer 1

Hint: The average velocity of an object is defined as its total displacement divided by the total time taken to cover the given displacement. In other words, it can also be defined as the rate at which an object changes its position from one place to another. Average velocity is a vector quantity and hence requires direction. The SI unit is meters per second. To solve this question, we first need to find the total displacement from the given data and then we can substitute it and the given time in the formula for the average velocity.

Complete step-by-step answer:

We know that the

\[\text{Distance=Speed} \times \text{time}\]

Displacement in x direction \[{{x}_{f}}=14\times 2=28m\]

Displacement in y direction\[{{y}_{f}}=8\times 5=40m\]

\[{{x}_{i}}=0,{{y}_{i}}=0\]

Where,

\[{{x}_{i}}\]= initial position in x direction

\[{{y}_{i}}\]= initial position in y direction

\[{{x}_{f}}\]= final position in x direction

\[{{y}_{f}}\]= final position in y direction

Total displacement is given by the formula \[\sqrt{\left( {{x}^{2}}+{{y}^{2}} \right)}\]

The total displacement \[=\sqrt{\left( {{28}^{2}}+{{40}^{2}} \right)}=48.8\,m\]

The total time taken is 10 seconds and the average velocity is the ratio of the total displacement to the total time taken.Now substituting these values in the formula given below we get,

Average velocity \[=\dfrac{Displacement}{time}\]

Average velocity \[=\dfrac{48.8}{10}=4.88m/s\approx 5m/s\]

Hence, the correct option is option B which is 5m/s in the north-east direction.

Note: Vector in physics is defined as a quantity that has both magnitude as well as direction. It is typically represented by an arrow whose direction is the same as that of the quantity and whose length is proportional to the magnitude of the quantity. Some examples of vector quantities are force, displacement, electric potential etc.