Use the equation for the motion of an accelerating object to answer the question. x=x0+v0t+12at2 Which equation could describe the motion of an object starting at x=0 with a starting speed of 10 m/s and an acceleration of 3 m/s2? (1 point) Responses x=5+3t x is equal to 5 plus 3 t x=1.5+10t x is equal to 1 point 5 plus 10 t x=10t+1.5t2 x is equal to 10 t plus 1 point 5 t squared x=3+5t2

Answer 1

To find the correct equation for the motion of the object starting at \( x = 0 \) with an initial speed \( v_0 = 10 , \text{m/s} \) and an acceleration \( a = 3 , \text{m/s}^2 \), we can use the equation:

\[ x = x_0 + v_0 t + \frac{1}{2} a t^2 \]

Given the values:

• \( x_0 = 0 \)
• \( v_0 = 10 \)
• \( a = 3 \)

Substituting these values into the equation gives:

\[ x = 0 + 10t + \frac{1}{2}(3)t^2 \]

This simplifies to:

\[ x = 10t + \frac{3}{2} t^2 \]

Note that \(\frac{3}{2} t^2\) can also be written as \(1.5t^2\), so the equation becomes:

\[ x = 10t + 1.5t^2 \]

So, the correct response, which describes the motion of the object, is:

\(x = 10t + 1.5t^2\)