Question

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Answer 1

Answer:

Question :-

$\mapsto$ A car travels a distance d on a straight road in two hours and then returns to the starting point in next three hours. What is the average speed.

Given :

$\mapsto$ A car travels a distance d on a straight road in two hours and then returns to the straight point in next three hours.

To Find :-

$\mapsto$ What is the average speed of a car.

Formula Used :-

$\clubsuit$ Average Speed Formula :

$\footnotesize\mapsto \sf\boxed{\bold{\pink{Average\: Speed =\: \dfrac{Total\: Distance\: Travelled}{Total\: Time\: Taken}}}}$

Solution :-

First, we have to find the total distance travelled :

$\leadsto$ A car travels a distance d on a straight road.

$\leadsto$ Again, after travelling d distance its returns to the straight point.

Hence, the total distance travelled is :

$\implies \sf Total\: Distance\: Travelled =\: d + d$

$\implies \sf\bold{\purple{Total\: Distance\: Travelled =\: 2d}}$

Now, again we have to find the total time taken :

$\leadsto$ A car travels a distance d on a straight road in 2 hours.

$\leadsto$ Again, the time taken to return the car in a initial position is 3 hours.

Hence, the total time taken is :

$\implies \sf Total\: Time\: Taken =\: 2 + 3$

$\implies \sf\bold{\purple{Total\: Time\: Taken =\: 5\: hours}}$

Now, we have to find the average speed of a car :

Given :

• Total distance travelled = 2d
• Total time taken = 5 hours

According to the question by using the formula we get,

$\footnotesize\longrightarrow \bf Average\: Speed =\: \dfrac{Total\: Distance\: Travelled}{Total\: Time\: Taken}$

$\longrightarrow \sf\bold{\red{Average\: Speed =\: \dfrac{2d}{5}}}$

${\small{\bold{\underline{\therefore\: The\: average\: speed\: of\: a\: car\: is\: \dfrac{2d}{5}\: .}}}}$

Hence, the correct options is option no (b) 2d/5.

Answer 2

Answer:

Option (B) is the correct answer.

$\large \: \: \: \: \: \green{ \boxed {\sf \: average \: speed \: \bar{v} = \frac{2d}{5} }} \:$

Explanation:

Method :

First, we have to find total distance and total time.

Cause, the formula of average speed is :

$\sf average \: \: speed \: \: \: \bar{v} \: = \frac{total \: distance \: (D)}{total \: time \: (T)}$

Solution :

First case :-

distance $d_1$ = d

time $t_1$ = 2 hrs

Second case :-

distance $d_2$ = d

time $t_2$ = 3 hrs

So,

$\sf \: total \: distance \: \: D = \: d_1 + d_2 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf\: = d + d \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 2d$

and

$\sf \: total \: time \: \: T = t_1 + t_2 \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 2 + 3 \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 5 \: hours$

So,

$\sf \: average \: speed \: \: \bar{v} \: = \frac{D}{T} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \sf \frac{2d}{5} \\ \\ \\ \large \: \: \: \: \: \green{ \boxed {\sf \therefore\: average \: speed \: \bar{v} = \frac{2d}{5} }}$