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

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