Question

Here's a question to test your physics!!
Saanvi while driving to school, computes the average speed for her trip to be 20 kilometre per hour. On her return trip along the same route, there is less traffic and the average speed is 30 kilometre per hour. what is the average speed for Saanvi's trip??​

Answer 1

Suppose the school is at a distance of x km.

While driving to school,the average speed is 20 km/h. Suppose the time taken while driving to school is t₁.

Now,

$\mapsto\sf{ Speed = \dfrac{Distance}{Time \: taken} }$

So,

$\mapsto \sf{ 20 = \dfrac{x}{t_{1}} }$

And,

$\mapsto \sf{ Time \: taken \: t _{1} = \dfrac{x}{20} }$

On return trip,the average speed is 30 km/h.Suppose the time taken for the trip is t₂.

Now,

$\mapsto\sf{ Speed = \dfrac{Distance}{Time \: taken} }$

So,

$\mapsto \sf{ 30 = \dfrac{x}{t_{2}} }$

And,

$\mapsto \sf{ Time \: taken \: t _{2} = \dfrac{x}{30} \: h}$

We will now consider the whole trip (going and coming back)

↦ Total distance (both ways) = x + x

↦ Total distance (both ways) = 2x km

And,

$\mapsto \sf{ \dfrac{x}{20} + \dfrac{x}{30} } \\ \\ \mapsto \sf{ \dfrac{3x + 2x}{60} } \\ \\ \mapsto \sf{ \dfrac{5x }{60} } \\ \\ \mapsto \sf{ \dfrac{x}{12} \: h }$

Now,

$\mapsto\sf{Average \: Speed = \dfrac{Total \: Distance \: Covered}{ Total\: Time \: Taken} } \\ \\ \mapsto \sf{ \dfrac{2x \times 12}{x} } \\ \\ \mapsto \sf{24 \: {km \: h}^{ - 1} }$

So,the average speed for Saanvi's trip is 24 kilometres per hour.

Answer 2

Answer :-

★ Average Speed for Saanvi's Journey = 24 Km/hr.

★ Concept :-

Here the concept of Average Speed has been used. According to this :-

$\bold{Average \: Speed_{(round\: the\: trip)}} = \\\\\:\:\: \bold{\dfrac{Total\: Distance}{Total\:Time}}$

• Distance = Speed × Time

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★ Question :-

Saanvi while driving to school, computes the average speed for her trip to be 20 kilometre per hour. On her return trip along the same route, there is less traffic and the average speed is 30 kilometre per hour. what is the average speed for Saanvi's trip ?

★ Solution :-

Let us solve this word problem line by line so that we can easily understand this. Here its give that :-

The trip contains going a distance then returning at same point. Then, Distance while going = Distance while returning. So,

» The distance covered = 2 × Distance while going

» Speed while going on journey = 20 Km/hr

» Speed while returning on from trip = 30 Km/hr

✒ Let the total distance covered while going be 'x' Km. Then, total distance while returning = x.

Now using above assumption,

» Total distance covered during journey = Distance covered while going + Distance covered while returning = x + x = 2x Km

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We already know that,

=> Distance = Speed × Time

So,

=> Time = Distance / Speed

Let us calculate the time taken for each trip now.

• Time taken for going is given as,

$\bold{Time (T_{1})} = \bold{\dfrac{x}{20}}\:  \bold{hr}$

• Time taken for returning is given as,

$\bold{Time (T_{2})} = \bold{\dfrac{x}{30}} \: \bold{hr}$

Then, total time = Time for going + Time for returning.

So,

✏ $\bold{Total\: Time} = \bold{\dfrac{x}{20}\: + \: \dfrac{x}{30}}$

✏ $\bold{Total\: Time} = \bold{\dfrac{(3x\: +\: 2x)}{60}}$

✏ $\bold{Total\: Time} = \bold{\dfrac{5x}{60}}$

✏ $\bold{Total\: Time\: Taken} = \bold{\dfrac{x}{12} \: }$

Now let us apply the given values and the values we got into our main equation of Average Speed.

✒ $\bold{Average \: Speed} = \bold{\dfrac{2x}{\dfrac{x}{12}}}$

Cancelling x from both numerator and denominator, we get,

✒ Average Speed = 2 × 12  Km/hr

✒ Average Speed = 24 Km/hr

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Hence, we get Average Speed for Saanvi's Journey = 24 Km/hr.

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★ More to know :-

• Speed = It is the rate of change of position of body in any direction. It is a scalar quantity. Its SI unit is m/s and its dimensional formula is [L¹/T¹].

• Uniform Speed = an object is said to be moving in uniform speed if ut covers equal distances in equal intervals of time, however small these time interval may be.

• Variable Speed us rge speed of a body if it covers unequal distances in equal intervals of time or vicé - versa.

• Average Speed is the speed of the body which is equal to the total distance travelled by the object divided by the total time taken to cover that distance.

• Instantaneous Speed = The speed of an object at any particular instant of time or at a particular point of its path is called the instantaneous speed of the object.