Question

a car travels 8m towards north with the speed of 2m/s and then 6m towards south with the speed of 3m/s. Find the magnitude of average velocity​

Answer 1

Explanation:

As per the provided information in the given question, we have :

• A car travels 8m towards north with the speed of 2m/s.
• Then, it travels 6m towards south with the speed of 3m/s.

We are asked to calculate the magnitude of average velocity.

Firstly, consider the diagram in the attachment.

Let us consider,

• A is its initial position.
• C is its final position.
• AB is length of path it travels towards North, 8 m.
• BC is length of path it travels towards south, 6 m.

We know that,

$\\ \longrightarrow \quad \pmb{\boxed{\sf{ Velocity_{(avg)} = \dfrac{Total \; displacement}{Total \; time} }}}$

★ Finding total displacement :

Displacement is the shortest distance from initial position to final position. Here, A is its initial position and C is its final position. Shortest distance between two positions is always a straight line. So, length of AC is the displacement.

We'll work out as per the diagram.

$\\ \longrightarrow \quad \sf { AC = AB - BC }$

$\\ \longrightarrow \quad \sf { AC = 8 \; m -6 \; m }$

$\\ \longrightarrow \quad \sf { AC = 2 \; m }$

$\\ \longrightarrow \quad \bf \underline { Total \; displacement = 2 \; m }$

★ Calculating total time :

$\\ \longrightarrow \quad \sf { Total \; time = t_1 + t_2 }$

• $\sf ( t_1)$ is time taken to cover the distance from A to B.
• $\sf ( t_2)$ is time taken to cover the distance from B to C.

We know that,

$\\ \longrightarrow \quad \pmb{\boxed{\sf{ Time = \dfrac{Distance}{Speed} }}}$

For $\sf ( t_1)$ :

>> Distance from A to B = 8 m

>> Speed attained to cover the distance from A to B = 2 m/s

For $\sf ( t_2)$ :

>> Distance from B to C = 6 m

>> Speed attained to cover the distance from B to C = 3 m/s

Now, substituting the values,

$\\ \longrightarrow \quad \sf { Total \; time = t_1 + t_2 }$

$\\ \longrightarrow \quad \sf { Total \; time = \Bigg ( \dfrac{8}{2} + \dfrac{6}{3} \Bigg) \; s }$

$\\ \longrightarrow \quad \sf { Total \; time = \Bigg ( 4 + 2 \Bigg) \; s }$

$\\ \longrightarrow \quad \bf \underline { Total \; times = 8 \; seconds }$

Now, substituting values in the formula of average velocity.

$\\ \longrightarrow \quad \pmb{\boxed{\sf{ Velocity_{(avg)} = \dfrac{Total \; displacement}{Total \; time} }}}$

$\\ \longrightarrow \quad \sf{ Velocity_{(avg)} = \dfrac{2 \; m}{8 \; s} }$

$\\ \longrightarrow \quad \sf{ Velocity_{(avg)} = \dfrac{1 \; m}{4 \; s} }$

$\\ \longrightarrow \quad \bf \underline{ Velocity_{(avg)} = 0.25 \; m/s }$

Therefore, magnitude of the average velocity is 0.25 m/s.