Question

H.W: 7. A car moves a distance of 200 m. It
covers that first half of the distance at speed
40 km/h and the second half of distance at
speed v. The average speed is 48 km/h. Find
the value of u.
(a) 56 km/h
(b) 60 km/h
(c) 50 km/h
(d) 48 km/h​

Answer 1

$v_{av}=\frac{u+v}{2}$

$48 = \frac{u+40}{2}$

u + 40 = 96

u = 96 - 40

u = 56

∴ the value of u is (a) 56 km/h

Answer 2

Given :-

Distance covered by the car = 200 m

Speed covered by the car in the first half = 40 km/h

Average speed of the car = 48 km/h

To Find :-

The value of 'v'.

Solution :-

We know that,

• s = Speed
• d = Distance
• t = Time

Using the formula,

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

Given that,

Distance (d) = 200 m (200 ÷ 2 = 100 m per half)

Speed (s) = 40 km/h

Average speed = 48 km/h

Substituting their values,

⇒ 48 = 200 / 100/4 + 100/v

⇒ 48 = 2 / 1/4 + 1/v

⇒ 48 = 1/40 + 1/v = 1/24

⇒ 1/v = 1/24 - 1/40

⇒ v = 5 - 3/120

⇒ v = 2/120

⇒ v = 60 km/h

Therefore, the value of 'v' is 60 km/h.