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18 June, 00:34

In fig. 2-27, a red car and a green car, identical except for the color, move toward each other in adjacent lanes and parallel to an x axis. at time t 0, the red car is at xr 0 and the green car is at xg 220 m. if the red car has a constant velocity of 20 km/h, the cars pass each other at x 44.5 m, and if it has a constant velocity of 40 km/h, they pass each other at x 76.6 m. what are (a) the initial velocity and (b) the constant acceleration of the green car?

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  1. 18 June, 00:48
    0
    The answer choice is 83
  2. 18 June, 00:50
    0
    a) V₀ = 13.5m/s

    b) a = 2.1 m/s²

    Explanation:

    1) Convert velocities to m/s

    i) 20 km/h * 1000m/kg * 1h/3600s = 5.556m/s

    ii) 40km/h = 11.111m/s

    2) Red car, time elapsed to reach position x = 44.5m

    Constant velocity ⇒ x = V*t ⇒ t = x / V

    ⇒ t₁ = 44.5m / 5.556m/s = 8s

    3) Red car, time elapsed to reach position x = 77.6m

    t₂ = 76.6m / 11.111/s = 6.9s

    4) Green car, distance run at t₁ = 8s, x = 44.5m

    i) uniform acceleration equation d = V₀t + at² / 2

    ii) d = 220m - x = 220m - 44.5m = 175.5m = V₀ (8) + a (8) ² / 2

    175.5 = 8V₀ + 32a ↔ equation (1)

    5) Green car, distance run at t₂ = 6.9s, x = 76.6m

    i) d = 220m - x = 220m - 76.6m = 143.4

    ii) 143.4 = V₀t₂ + at₂² / 2

    143.4 = V₀ (6.9) + a (6.9) ² / 2

    143.4 = 6.9V₀ + 23.8a ↔ equation (2)

    6) Solve the system of equations:

    175.5 = 8V₀ + 32a ↔ equation (1)

    143.4 = 6.9V₀ + 23.8a ↔ equation (2)

    V₀ = 13.5m/s

    a = 2.1 m/s²
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