A 104 horse-power suv speeds up from 21 m/s to 29 m/s in 3 seconds, what is the mass of the suv?

Correct answer: m = 1,160 kg

Explanation:

Given:

P = 104 hp = 77.48 kW = 77.48 · 10³ W

V₁ = 21 m/s Initial speed (velocity)

V₂ = 29 m/s Final speed (velocity)

t = 3 seconds The time interval during which the work was performed

m = ?

The formula for calculating power is:

P = A / Δt

Since work is a measure of energy change in this case kinetic:

P = ΔEk / Δt = (Ek₂ - Ek₁) / Δt = (m V₂² / 2 - m V₁² / 2) / Δt

P = m · (V₂² - V₁²) / 2 · Δt ⇒ m = (2 · P · Δt) / (V₂² - V₁²)

m = (2 · 77.48 · 10³ · 3) / (29² - 21²) = 464.88 · 10³ / (841 - 441)

m = 464.88 · 10³ / 400 = 1.16 · 10³ = 1,160 kg

m = 1,160 kg

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