Answer: the acceleration of the object is 4 m/s^2.
Explanation: To determine the acceleration of the object, we can use the work-energy principle, which states that the work done on an object is equal to its change in kinetic energy. The equation for the work-energy principle is:
W = ΔKE = (1/2)mv^2 - (1/2)mu^2
where W is the work done, ΔKE is the change in kinetic energy, m is the mass of the object, v is the final velocity of the object, and u is the initial velocity of the object (which we assume to be zero).
We can rearrange this equation to solve for the final velocity v:
v^2 = (2W/m) + u^2
Since the initial velocity is zero, this simplifies to:
v^2 = 2W/m
Now, we can use the equation for average acceleration:
a = (v - u) / t
where t is the time taken to travel the distance of 50m. Assuming that the object starts from rest, u = 0, and the equation simplifies to:
a = v / t
Substituting the expression for v, we get:
a = sqrt(2W/m) / t
Plugging in the given values of W = 400 J, m = 2 kg, and t = 50 m / v (since t = d/v), we get:
a = sqrt(2*400 J / 2 kg) / (50 m / v)
a = sqrt(400 m^2/s^2) / (50 m / v)
a = 4 m/s^2
Therefore, the acceleration of the object is 4 m/s^2.
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