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Question

A car accelerates with a constant acceleration for 8 seconds before reaching top speed. The car completes a trip of 0.9 kilometer in a total travel time of 47 seconds (including the time it takes to reach the top speed). What is the final speed (in km/h) at which car completes the trip if it maintained the top speed for the entire remaining part of the journey?

Answer 1

1st part of trip is constant acceleration (a₁) for a time, t₁ = 8s and an initial v₀ = 0

2nd part of trip is constant velocity, v₁ = v₂ for a time, t₂ = 47s

Total trip has d_T = 900 m. What is v₁ = v₂?

applicable equations: d₁ = (1/2)a₁t₁² and v₁ = a₁t₁ for constant acceleration from rest

d₂ = v₁t₂

d_tot = d₁ + d₂

We have 4 unknowns and 4 equations, let's use the last equation with the other equations to plug in for d₁,d₂, and a₁ for an equation in v₁

d_Tot = (1/2)(v₁/t₁)t₁² + v₁t₂ or v₁ = d_Tot/(t₁/2 + t₂) = 900 m/(8/2 + 47 s)

You have to convert to km/hr.

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