Question

A train covers first 10 km with speed 2km/h and next 20 km with speed 5km/h. Calculate average speed and average velocity of the train.

Answer 1

QUESTION:-

A train covers first 10 km with speed 2km/h and next 20 km with speed 5km/h. Calculate average speed and average velocity of the train.

EXPLANATION:-

$\bold{we\:know\:that\:v_a_v_g=\frac{total\:distance}{total\:time}}$

So here total distance is=10 km +20 km $\bold{t_1}=\bold{\frac{10}{2}}$

So total distance =30 km

And here time is not given ,so we have to calculate the time using the formula:-

$\bold{time=\frac{distance}{speed}} \:or\: \bold{t=\frac{d}{s}}$

So here we have to calculate 2 times as two distance and two speed of the train is given.

Let's say Time taken to cover first distance be=$\bold{t_1}$

and time taken to cover 2nd distance be=$\bold{t_2}$

So let's calculate both the times:-$\bold{t_1}=\bold{\frac{10}{2}}$

$\bold{t_1}=\bold{5\:hours}$

Similarly $\bold{t_2}=\bold{\frac{20}{5}}$

$\bold{t_2}=\bold{4\:hours}$

Total time=5+4=9 hours

Now we know the total distance and total time ,let's apply it in formulae

$\bold{v_a_v_g=\frac{30}{9}}$

$\bold{v_a_v_g}=\bold{3.333}$

So the average speed is 3.333 km/hr

$\rule{300}{1.5}$