Two towns are at a distance of 240 km from each other. A motorist takes 8 hours to cover the distance if he travels at a speed of V1 km/h from town A to an intermediate town C, and then continues on his way with an acceleration of x km/hr^2. He needs the same time to cover the whole distance if he travels from A to C at V1 km/h and from C to B at V2 km/h or from A to C at V2 km/h and from C to B at V1 km/h. Find V1 if the acceleration 'x' is double V1 in magnitude and V1 IS NOT EQUALS TO V2.
(a) 15 km/h
(b) 10 km/h
(c) 20 km/h
(d) 8 km/h
Answers
Subtraction with conversion
(a) 15 km 757m from 20 Km [ convert to metre]
Given : Two towns are at a distance of 240 km from each other.
A motorist takes 8 hours to cover the distance
he travels at a speed of V1 km/h from town A to an intermediate town C, and then continues on his way with an acceleration of x km/hr^2.
acceleration 'x' is double V1 in magnitude
V₂ ≠ V₁
To Find : V₁
Solution:
Let say distance form A to C = d km
Distance from C to B = 240 - d km
d/V₁ + (240 - d)/V₂ = d/V₂ + (240 - d)/V₁
=> (d - 240 + d)/V₁ = ( d - 240 + d)/V₂
=> (2d - 240)V₂ = (2d - 240)V₁
=> (2d - 240) ( V₂ - V₁) = 0
V₂ - V₁ ≠ 0 ∵ V₂ ≠ V₁
=> 2d - 240 = 0
=> d = 120
120/V₁ = t₁
t₂ = 8 - t₁
S = ut + (1/2)at²
120 = V₁t₂ + (1/2)x(t₂)²
=> 120 = V₁ ( 8 - t₁) + (1/2)(2V₁) ( 8 - t₁)²
=> 120 = 8V₁ - V₁t₁ + V₁(t² -16t + 64)
=> 120 = 8V₁ - 120 + 120t₁ - 16(120) + 64V₁
=> 18 (120) = 72V₁ + 120t₁
=> 180 = 6V₁ + 10t₁
=> 180 = 6V₁ + 10(120/V₁)
=> 180V₁ = 6V₁² + 1200
=> V₁² - 30V₁ + 200 = 0
=> V₁² - 20V₁ - 10V₁ + 200 = 0
=> V₁ = 20 or 10
V₁ = 10 is not possible as then it will take 10 hrs to
Hence V₁ = 20
20 km/h is the correct answer
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