Final answer:
To find the value of V₀ in the given scenario, we can use the kinematic equation for deceleration, which involves the total distance traveled and the initial deceleration. After plugging in the values and solving the equation, we find that the value of V₀ is approximately 89.44 m/s. So, none of the given options are correct.
Step-by-step explanation:
To find the value of V₀, we can use the kinematic equation for deceleration: V² = V₀² + 2aΔx.
In this case, the total distance traveled is 4 km, so Δx = 4 km = 4000 m.
The initial deceleration is given as 4 m/s². Plugging these values into the equation, we get:
V² = V₀² + 2(4 m/s²)(4000 m)
V² = V₀² + 8000 m²/s²
Since the initial velocity, V₀, is what we are trying to find, we can rearrange the equation to solve for V₀:
V₀² = V² - 8000 m²/s²
V₀² = (0 m/s)² - 8000 m²/s²
V₀ = ±√(-8000)
Since velocity cannot be a negative value, we can ignore the negative solution. Therefore, the value of V₀ is approximately equal to 89.44 m/s.
None of the given options are correct.
Question: Given that the total distance traveled is 4 km and the initial deceleration is 4 m/s², find: the value of V₀?
a) 2 m/s
b) 4 m/s
c) 6 m/s
d) 8 m/s