Question

8. A bus travels on a straight road for 40km at 30kmph. It then continues in the
same direction for another 40km at 60kmph.
(a) What is the average velocity of the bus during the entire journey?
(b) What is the average speed during the entire journey?​

Answer 1

Answer:

Average speed = 40 km/h

Average velocity = 40 km/h

Explanation:

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

• A bus travels on a straight road for 40km at 30km/h.
• It then continues in the same direction for another 40km at 60km/h.

We are asked to calculate average velocity and average speed during the entire journey.

★ Calculating average speed :

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

Finding total distance travelled :

$\\ \longrightarrow \quad \sf { Total \; distance = 40 \; km + 40 \; km}$

$\\ \longrightarrow \quad \bf \underline{ Total \; distance = 80 \; km}$

Finding total time :

In first 40 km, it travels with the speed of 30 km/h, so time taken to cover first 40 km :

$\\ \longrightarrow \quad \pmb {\boxed{\sf{ Time \; (t_1) = \dfrac{Distance}{Speed} }}}$

• Distance = 40 km
• Speed = 30 km/h

$\\ \longrightarrow \quad \sf { Time \; (t_1) = \dfrac{40}{30} \; hr }$

Now, in next 40 km, it travels with the speed of 60 km/h, so time taken to cover next 40 km :

$\\ \longrightarrow \quad \pmb {\boxed{\sf{ Time \; (t_2) = \dfrac{Distance}{Speed} }}}$

• Distance = 40 km
• Speed = 60 km/h

$\\ \longrightarrow \quad \sf { Time \; (t_2) = \dfrac{40}{60} \; hr }$

Therefore,

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

$\\ \longrightarrow \quad \sf { Total \; time =\dfrac{40}{30} \; hr + \dfrac{40}{60} \; hr }$

$\\ \longrightarrow \quad \sf { Total \; time =\dfrac{80+40}{60} \; hr }$

$\\ \longrightarrow \quad \sf { Total \; time =\dfrac{120}{60} \; hr }$

$\\ \longrightarrow \quad \bf \underline{ Total \; time = 2 \; hr }$

Substituting the values in the formula of average speed.

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

$\\ \longrightarrow \quad \sf { Speed_{(avg)} =\dfrac{80}{2} \; km/h }$

$\\ \longrightarrow \quad \bf \underline { Speed_{(avg)} = 40 \; km/ h }$

Therefore, average speed of the bus is 40 km.

★ Calculating average velocity :

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

Finding total displacement :

Total displacement simply means the displacement. When the body moves in a single straight line without changing the direction,then the magnitude of displacement and distance are same.

Here, the bus hasn't changed it direction and covered the distance in a single straight line. So, here the displacement will be equal to the distance.

$\\ \longrightarrow \quad \bf \underline{ Displacement = 80 \; km }$

We have the value of total time. Substituting values,

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

$\\ \longrightarrow \quad \sf { Velocity_{(avg)} =\dfrac{80}{2} \; km/ h }$

$\\ \longrightarrow \quad \bf \underline { Velocity_{(avg)} = 40 \; km/ h }$

Therefore, average velocity of the bus is 40 km/h.

Answer 2

Answer:

Average speed : 40 km/h

Average velocity : 40 km/h