1. Kinematics

Motion With Variable Acceleration — Quiz

Test your understanding of motion with variable acceleration with 5 practice questions.

Practice Questions

Question 1

A particle moves along the x-axis with an acceleration given by $a(t) = 6t - 12 \text{ m/s}^2$. If the particle starts from rest ($v(0) = 0$) at the origin ($x(0) = 0$), what is its position at $t = 2 \text{ s}$?

Question 2

The velocity of a particle is given by $v(x) = kx^2$, where $k$ is a positive constant. If its initial position is $x(0) = x_0$, which of the following expressions correctly describes the position as a function of time, $x(t)$?

Question 3

A particle's acceleration is given by $a(v) = -bv$, where $b$ is a positive constant. If its initial velocity is $v_0$, what is the time it takes for the particle's velocity to reduce to half of its initial value?

Question 4

If the acceleration of a particle is given by $a(x) = -kx$, where $k$ is a positive constant, and its initial position is $x_0$ and initial velocity is $v_0$, which of the following expressions correctly describes the velocity as a function of position, $v(x)$?

Question 5

A particle's acceleration is given by $a(v) = -c v^2$, where $c$ is a positive constant. If its initial velocity is $v_0$, which of the following expressions correctly describes the velocity as a function of time, $v(t)$?