Question

A truck moves a distance of 50 km it covers first half of the distance at speed of 200 m per second and second half at speed V if average speed of truck is hundred metre per second then the value of V is?

Answer 1

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Answer 2

Answer:

The truck covers the second half of the distance at speed of 66.67 m/s.

Explanation:

Given that,

Average speed = 100 m/s

Total distance d = 50 km = 50000 m

Velocity for first half of the distance = 200 m/s

Velocity of second half of the distance = V m/s

We know that,

The formula of time

The time in first half of the distance

$t = \dfrac{d}{v}$

Where, d = distance

v = speed

Put the value of v and d in the formula

$t_{1}=\dfrac{25000}{200}$

$t_{1}=125\ sec$

Now, The time in second half of the distance

$t_{2}=\dfrac{25000}{V}$

The average speed of the truck is

$V_{av}=\dfrac{D}{T}$

Where, $V_{av}$ = average speed

D = total distance

T = total time

$V_{av}=\dfrac{D}{t_{1}+t_{2}}$

We substitute the value in the formula

$100=\dfrac{50000}{125+\dfrac{25000}{V}}$

$100=\dfrac{125}{125}\times(\dfrac{400V}{V+200})$

$100=\dfrac{400}{V+200}$

$100V+20000=400V$

$V = \dfrac{20000}{300}$

$V = 66.67\ m/s$

Hence, The truck covers the second half of the distance at speed of 66.67 m/s.