Question

1. - / 1 pointsa particle moves in a straight line with an initial velocity of 19 m/s and a constant acceleration of $26\\ \text{m/s}^2$. if $t = 0$, $x = 0$, what is the particles position (in m) at $t = 4\\ \text{s}$?enter a number.mdetailsmy notesask your teacherpractice anotherresourcesreading

Explanation:

Step1: Select kinematic position formula

The position of an object under constant acceleration is given by:
$$x(t) = x_0 + v_0 t + \frac{1}{2} a t^2$$

Step2: Identify given values

$x_0 = 0\ \text{m}$, $v_0 = 19\ \text{m/s}$, $a = 26\ \text{m/s}^2$, $t = 4\ \text{s}$

Step3: Substitute values into formula

$$x(4) = 0 + (19)(4) + \frac{1}{2}(26)(4)^2$$

Step4: Calculate each term

$$(19)(4) = 76,\quad \frac{1}{2}(26)(16) = 208$$

Step5: Sum the terms

$$x(4) = 76 + 208$$

Answer:

284