To find the force responsible for the acceleration of the shopping cart, we can use Newton's second law of motion, which states that \( F = ma \), where \( F \) is the force, \( m \) is the mass, and \( a \) is the acceleration.
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Determine the acceleration \( a \): We can use the formula for acceleration, which is given by: \[ a = \frac{\Delta v}{\Delta t} \] where \( \Delta v \) is the change in velocity and \( \Delta t \) is the time taken. The change in velocity is: \[ \Delta v = v_f - v_i = 4.0 , \text{m/s} - 0 , \text{m/s} = 4.0 , \text{m/s} \] The time taken is \( \Delta t = 0.5 , \text{s} \).
Now we can calculate the acceleration: \[ a = \frac{4.0 , \text{m/s}}{0.5 , \text{s}} = 8.0 , \text{m/s}^2 \]
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Calculate the force \( F \): We now use the mass of the shopping cart, which is \( m = 8.0 , \text{kg} \), to find the force: \[ F = m \cdot a \] Substituting the values we have: \[ F = 8.0 , \text{kg} \cdot 8.0 , \text{m/s}^2 = 64.0 , \text{N} \]
Therefore, the magnitude of the force responsible for the acceleration of the shopping cart is \( \boxed{64.0} , \text{N} \).
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