Kinematics with calculus Knowledge-Based Practice

Questions

1. 1.

   A particle moves along a straight line with an acceleration given by $a(x) = 6x$, where $a$ is in meters per second squared and $x$ is in meters. If its speed is 4 m/s at $x = 1$ m, what is its speed at $x = 3$ m?

   • A) 6 m/s
   • B) 7 m/s
   • C) 8 m/s
   • D) 10 m/s
2. 2.

   A particle moves along the $x$-axis with a velocity given by $v(t) = 6 - 2t$, where $v$ is in meters per second and $t$ is in seconds. What is the total distance traveled by the particle from $t = 0$ s to $t = 5$ s?

   • A) 13 m
   • B) 5 m
   • C) 9 m
   • D) 17 m
3. 3.

   A particle moves along a straight line such that its position as a function of time is given by $x(t) = \frac{1}{3}t^3 - 3t^2 + 5t + 8$, where $x$ is in meters and $t \ge 0$ is in seconds. What is the velocity of the particle at the instant its acceleration is zero?

   • A) 5 m/s
   • B) 0 m/s
   • C) 4 m/s
   • D) -4 m/s
4. 4.

   An object moves along a straight path with an acceleration given by $a(t) = 6t - 2$ m/s$^2$, where $t$ is in seconds. If its velocity is 4 m/s and its position is 5 m at $t = 0$ s, what is its position at $t = 2$ s?

   • A) 17 m
   • B) 12 m
   • C) 21 m
   • D) 9 m
5. 5.

   A particle moves along a straight line such that its velocity is given by $v(t) = 3t^2 - 12t + 9$ m/s, where $t$ is time in seconds. What is the particle's acceleration at the earliest time $t \ge 0$ when it momentarily comes to rest?

   • A) -12 m/s²
   • B) -6 m/s²
   • C) 0 m/s²
   • D) 6 m/s²

Answers and step-by-step solutions appear after you finish the test.