Question

A car moves from A to B at a speed of 60km/hr and returns from B to A at 100km/hr . Find average speed and average velocity ?​

Answer 1

Answer:

$\boxed{ \sf Average \: speed \ of \ car = 75 \: km/h}$

$\boxed{\sf Average \ velocity = 0 \ km/h}$

Given:

Speed of car from A to B = 60 km/h

Speed of B to A = 100 km/h

To find:

(i) Average speed of car

(ii) Average velocity of car

Explanation:

(i) Let distance between A to B be 'd'

So, Total distance travelled by car = 2d

Let the time taken to travel from A to B be $\sf t_{1}$

As, we know

$\sf speed = \frac{distance}{time}$

Therefore,

$\sf \implies 60 = \frac{d}{t_{1}} \\ \\ \sf \implies t_{1} = \frac{d}{60}$

Let the time taken to travel from B to A be $\sf t_{2}$

Therefore,

$\sf \implies 100 = \frac{d}{ t_{2}} \\ \\ \sf \implies t_{2} = \frac{d}{100}$

Total time for covering 2d distance (t) = $\sf t_{1} + t_{2}$

$\sf Average \: speed = \frac{Total \: distance}{Total \: time} \\ \\ \sf = \frac{2d}{t} \\ \\ \sf = \frac{2d}{t_{1} + t_{2}} \\ \\ \sf = \frac{2d}{ \frac{d}{60} + \frac{d}{100} } \\ \\ \sf = \frac{2d}{ \frac{5d}{300} + \frac{3d}{300} } \\ \\ \sf = \frac{2d}{ \frac{5d + 3d}{300} } \\ \\ \sf = \frac{2d}{ \frac{8d}{300} } \\ \\ \sf = \frac{2 \cancel{d} \times 300}{8 \cancel{d}} \\ \\ \sf = \frac{\cancel{2} \times 300}{4 \times \cancel{2}} \\ \\ = \sf \frac{300}{4} \\ \\ \sf = \frac{75 \times \cancel{4}}{\cancel{4}} \\ \\ \sf = 75 \: km/h$

(ii) As the car returns to it's initial position i.e. A therefore;

Displacement of car = 0

$\sf Average \ velocity = \frac{Displacement}{Total \ time} \\ \\ \sf = \frac{0}{t} \\ \\ \sf = 0 \ km/h$

Answer 2

Given :-

• Speed of car moving A to B = 60km/h

• And Again speed of returning B to A = 100km/h

To Find:-

• Average Speed

• Average velocity.

Solution :-

Let, the distance from A to B = x

∴ The total distance covered by car =x+x =

2x

Time taken by car to moving A to B = 60/x

and,

time taken by car to returning B to A = 100/x

➦ Average speed = Total distance /total time taken

➭ Av. Speed = 2x/60/x+100/x

➭ Av. Speed = 2x/60 +100/x

➭ Av. Speed = 160/2

➭ Av. speed= 80km/h

∴ The average speed of car is 80km/h

Now,

The car start from A and go to B and again return to A

∴ The displacement of car =0

➦Average velocity = total displacement/total time taken

➭ Av. velocity = 0/60/x+100/x

➭ Av. velocity = 0 km/h

∴ The average velocity of car is 0 km/h