To determine the total distance traveled by the car, we can use the kinematic equations of motion. The car is initially moving at a speed of \( v_0 = 5.0 , \text{m/s} \) and is experiencing a uniform acceleration \( a = 2.0 , \text{m/s}^2 \) over a time interval \( t = 10 , \text{s} \).
We use the following kinematic equation to calculate the distance traveled:
\[ d = v_0 t + \frac{1}{2} a t^2 \]
Substituting the known values into the equation:
\[ d = (5.0 , \text{m/s})(10 , \text{s}) + \frac{1}{2}(2.0 , \text{m/s}^2)(10 , \text{s})^2 \]
Calculating each term separately:
- \( v_0 t = (5.0 , \text{m/s})(10 , \text{s}) = 50.0 , \text{m} \)
- \( \frac{1}{2} a t^2 = \frac{1}{2}(2.0 , \text{m/s}^2)(100 , \text{s}^2) = 1.0 \times 100 , \text{m} = 100.0 , \text{m} \)
Now, add the two distances together:
\[ d = 50.0 , \text{m} + 100.0 , \text{m} = 150.0 , \text{m} \]
Therefore, the total distance traveled by the car during the 10-second interval is \( \boxed{150.0 , \text{m}} \).
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