Question

use the equation for the motion of an accelerating object to answer the question.
x = x₀ + v₀t + \frac{1}{2}at²
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)
\bigcirc x = 5 + 3t
\bigcirc x = 3 + 5t²
\bigcirc x = 1.5 + 10t
\bigcirc x = 10t + 1.5t²

Explanation:

Step1: Substitute \(x_0 = 0\) into the equation

Given \(x=x_0 + v_0t+\frac{1}{2}at^2\), when \(x_0 = 0\), the equation becomes \(x=v_0t+\frac{1}{2}at^2\)

Step2: Substitute \(v_0 = 10\) and \(a = 3\)

We know that \(v_0 = 10\) and \(a = 3\). Then \(\frac{1}{2}a=\frac{1}{2}\times3 = 1.5\)
Substituting these values into \(x=v_0t+\frac{1}{2}at^2\), we get \(x = 10t+1.5t^2\)

Answer:

\(x = 10t + 1.5t^2\) (the fourth option)