Question

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

Answer 1

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**