Question

If the resistance R Newton's to the motion of a moving vehicle varies directly as the square of the speed V km/hr, write down the relation between R and V. Given that R 600 Newton's when V =20 find the ,

(1). Speed when the resistance is 3375 Newton's
(2).resistance given that the speed is 32 Km/hr​

Answer 1

see explanation

Explanation:

Given that R varies directly as v² then the equation relating them is

R = kv² ← k is the constant of variation

To find k use the condition R = 600 when v = 20

k =
`(R)/(v^2)` =
`(600)/(20^2)` =
`(600)/(400)` = 1.5

R = 1.5v² ← equation of variation

(1)

When R = 3375, then

3375 = 1.5v² ( divide both sides by 1.5 )

2250 = v² ( take the square root of both sides )

v =
`√(2250)` ≈ 47.43 Km/hr

(2)

When v = 32, then

R = 1.5 × 32² = 1.5 ×1024 = 1536 N