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)

The velocity function \(v(t)\) is the first derivative of the position function \(x(t)\).
\(v(t) = x'(t) = \frac{d}{dt}(7t - 3) = 7\)

Step2: Find acceleration (2nd derivative)

The acceleration function \(a(t)\) is the first derivative of the velocity function \(v(t)\).
\(a(t) = v'(t) = \frac{d}{dt}(7) = 0\)

Step3: Evaluate at \(t=6\)

Since acceleration is constant, it is the same for all \(t\geq0\).
\(a(6) = 0\)

Answer:

0