Kinematics with calculus Knowledge-Based Download PDF

Questions

1. 1.

   A particle moves along the $x$-axis with an acceleration given by $a(t) = 6t - 4$, where $a$ is in meters per second squared and $t$ is in seconds. If the particle's initial velocity is 5 m/s and its initial position is 2 m at $t = 0$, what is the position of the particle at $t = 3\text{ s}$?

   • A) 14 m
   • B) 20 m
   • C) 26 m
   • D) 38 m
2. 2.

   The position of an object moving along the $x$-axis is given by $x(t) = 2t^3 - 9t^2 + 12t - 4$, where $x$ is in meters and $t$ is in seconds. What is the acceleration of the object at the later time when its velocity is momentarily zero?

   • A) $-18\text{ m/s}^2$
   • B) $-6\text{ m/s}^2$
   • C) $6\text{ m/s}^2$
   • D) $12\text{ m/s}^2$