Question

A train takes 2 hr to reach station B from station A, and then 3 hr to return from station B to station A. The distance between the two stations is 200 km. Find: (i) The average speed

Answer 1

Answer:

average speed is 23.15 m/s^2

Explanation:

Let u and v be the speed of the train from A to B and from B to A respectively.

here,

distance (d)= 200 km =20× 1000m=20,000m,

Time taken from A to B (p) = 2 hrs = 2×60×60 seconds= 7200 seconds,

Time taken from B to A (q) = 3 hours = 3×60×60 seconds= 10,800 seconds

hence,

$u=\frac{d}{p} \\u=\frac{ 200000 }{7200}$    ∴ u = 27.78 m/s^2

$v=\frac{d}{q}\\ v=\frac{200000}{10800}$   ∴v = 18.52 m/s^2

let z be the average speed,

z= (27.78+18.52)/2

∴z= 23.15

hence the average speed is 23.15 m/s^2

Answer 2

$\large{\underline{\rm{\orange{\bf{Given:-}}}}}$

Time taken to reach station B from station A = 2 hour

Time taken to return from station B to station A = 3 hour

Distance between the two stations = 200 km

$\large{\underline{\rm{\orange{\bf{To \: Find:-}}}}}$

The average speed.

$\large{\underline{\rm{\orange{\bf{Analysis:-}}}}}$

$\sf Average \: speed=\dfrac{Total \: distance}{Total \: time}$

$\large{\underline{\rm{\orange{\bf{Solution:-}}}}}$

We know that,

• t = Time
• d = Distance

Given that,

A train takes 2 hours to reach station b from station a,  and then 3 hours to return from station b to station a.

Total distance (d) = 200 + 200

Total distance (d) = 400 km

Total time (t) = 2 + 3

Total time (t) = 5 hours

$\boxed{\sf Average \: speed=\dfrac{Total \: distance}{Total \: time}}$

Substituting their values,

Average speed = $\sf \dfrac{400}{5} \: km$

Average speed = 80 km/h

Therefore, the average speed is 80 km/h

$\large{\underline{\rm{\orange{\bf{To \: Note:-}}}}}$

Speed is the rate of change of distance with time.  As a scalar it has magnitude only.

Average speed is measured over a non-zero time interval.

Speed, being a scalar quantity, is the rate at which an object covers distance. The average speed is the distance (a scalar quantity) per time ratio.

When the speed does not change it is constant.  For constant speed, the average and instantaneous speeds are the same.