An object traveling along the x-axis with constant acceleration has velocity v = +11.0 m/s when it is at x = 6.0 m and v = +20.0 m/s when it is at x = 10.0 m. What is its acceleration?
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To find the acceleration of the object, we can use the equation of motion that relates velocity, initial velocity, acceleration, and displacement:
v^2 = u^2 + 2aΔx
Where:
v = final velocity = +20.0 m/s
u = initial velocity = +11.0 m/s
a = acceleration (unknown)
Δx = displacement = x2 - x1 = (10.0 m - 6.0 m) = 4.0 m
Substituting the given values into the equation, we have:
(20.0 m/s)^2 = (11.0 m/s)^2 + 2a(4.0 m)
400 m^2/s^2 = 121 m^2/s^2 + 8a
Subtracting 121 m^2/s^2 from both sides:
279 m^2/s^2 = 8a
Finally, dividing both sides by 8:
a = 279 m^2/s^2 / 8
Therefore, the acceleration of the object is approximately 34.875 m/s^2.