Question

a particle moves along the $x$-axis. the function $x(t)$ gives the particles position at any time $t \geq 0$

$x(t) = 7t - 3$

what is the particles acceleration $a(t)$ at $t = 6$
$a(6) = \square$

Explanation:

Step1: Find velocity (1st derivative)

Velocity $v(t)$ is the derivative of position $x(t)$:
$v(t) = \frac{d}{dt}(7t - 3) = 7$

Step2: Find acceleration (2nd derivative)

Acceleration $a(t)$ is the derivative of velocity $v(t)$:
$a(t) = \frac{d}{dt}(7) = 0$

Step3: Evaluate at $t=6$

Acceleration is constant for all $t$, so:
$a(6) = 0$

Answer:

$0$