To describe the motion of an object starting at \( x = 0 \) with an initial speed of \( v_0 = 10 \) m/s and an acceleration of \( a = 3 \) m/s², you can use the equation:
\[ x = x_0 + v_0 t + \frac{1}{2} a t^2 \]
where:
- \( x_0 \) is the initial position (0 in this case),
- \( v_0 \) is the initial velocity (10 m/s),
- \( a \) is the acceleration (3 m/s²), and
- \( t \) is time.
Substituting in the values:
\[ x = 0 + 10t + \frac{1}{2} (3) t^2 \]
Calculating \( \frac{1}{2} (3) t^2 \):
\[ \frac{1}{2} (3) t^2 = 1.5t^2 \]
Now, putting everything together:
\[ x = 10t + 1.5t^2 \]
Thus, the equation that describes the motion of the object is:
\[ x = 10t + 1.5t^2 \]
From the given responses, the correct answer is:
x = 10t + 1.5t².
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