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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=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

1 answer

To find the equation that describes the motion of the object, we can use the formula:

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

Given:

  • Starting position \( x_0 = 0 \)
  • Starting speed \( v_0 = 10 , \text{m/s} \)
  • Acceleration \( a = 3 , \text{m/s}^2 \)

Substituting these values into the equation:

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

This simplifies to:

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

Now, \(\frac{3}{2}t^2 = 1.5t^2\), so we can rewrite it as:

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

Looking at the response options:

  1. x = 1.5 + 10t (Incorrect, doesn't match)
  2. x = 10t + 1.5t^2 (Correct, matches the derived equation)
  3. x = 3 + 5t^2 (Incorrect, doesn't match)

The correct response is:

x = 10t + 1.5t^2