Question

Use the equation for the motion of an accelerating object to answer the question.

x=x0+v0t+1/2at^2

Which equation could describe the motion of an object starting at x=0
𝑥
=
0
with a starting speed of 10 m/s and an acceleration of 3 m/s2?

(1 point)
Responses

x=3+5t^2

x=5+3t

x=1.5+10t


x=10t+1.5t2

Answer 1

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**.