andrewdaniel1987
andrewdaniel1987 Jan 17, 2026 • 0 views

Position, Velocity, and Acceleration Vectors Quiz with Answer Key

Hey there! 👋 Getting your head around position, velocity, and acceleration vectors can be tricky, but don't worry, I've got you covered! This guide will help you ace your physics quiz. Let's dive in! 🚀
⚛️ Physics

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john_huerta Dec 31, 2025

📚 Quick Study Guide

  • 📍 Position Vector: Describes the location of an object in space relative to an origin.
  • 🚗 Velocity Vector: Represents the rate of change of position with respect to time, including both speed and direction. Formula: $\vec{v} = \frac{d\vec{r}}{dt}$
  • 💨 Acceleration Vector: Represents the rate of change of velocity with respect to time. Formula: $\vec{a} = \frac{d\vec{v}}{dt}$
  • 📐 Vector Components: Vectors can be broken down into components along coordinate axes (e.g., x, y, z).
  • Vector Addition/Subtraction: Use component-wise addition/subtraction.
  • 💡 Constant Acceleration Equations: Useful when acceleration is constant. For example, $\vec{v} = \vec{v_0} + \vec{a}t$ and $\vec{r} = \vec{r_0} + \vec{v_0}t + \frac{1}{2}\vec{a}t^2$

🧪 Practice Quiz

  1. A particle's position vector is given by $\vec{r} = (3t^2)\hat{i} - (6t)\hat{j}$ (meters), where t is in seconds. What is the velocity vector at t = 2s?
    1. (12$\hat{i}$ - 6$\hat{j}$) m/s
    2. (6$\hat{i}$ - 6$\hat{j}$) m/s
    3. (3$\hat{i}$ - 6$\hat{j}$) m/s
    4. (12$\hat{i}$ + 6$\hat{j}$) m/s
  2. An object moves with a constant acceleration of $\vec{a} = (2\hat{i} + 3\hat{j})$ m/s². If its initial velocity is $\vec{v_0} = (\hat{i} - \hat{j})$ m/s, what is its velocity after 3 seconds?
    1. (7$\hat{i}$ + 8$\hat{j}$) m/s
    2. (6$\hat{i}$ + 9$\hat{j}$) m/s
    3. (7$\hat{i}$ + 9$\hat{j}$) m/s
    4. (5$\hat{i}$ + 8$\hat{j}$) m/s
  3. A car accelerates from rest with a constant acceleration of $\vec{a} = (4\hat{i})$ m/s². What is its displacement vector after 5 seconds?
    1. (50$\hat{i}$) m
    2. (10$\hat{i}$) m
    3. (20$\hat{i}$) m
    4. (100$\hat{i}$) m
  4. A projectile is launched with an initial velocity of $\vec{v_0} = (10\hat{i} + 20\hat{j})$ m/s. Assuming no air resistance, what is the acceleration vector during its flight?
    1. (0$\hat{i}$ - 9.8$\hat{j}$) m/s²
    2. (10$\hat{i}$ - 9.8$\hat{j}$) m/s²
    3. (0$\hat{i}$ + 9.8$\hat{j}$) m/s²
    4. (9.8$\hat{i}$ + 0$\hat{j}$) m/s²
  5. If the position vector of an object is given by $\vec{r}(t) = (2t^3 - t)\hat{i} + (3t^2)\hat{j}$, what is the acceleration vector at t = 1 second?
    1. (12$\hat{i}$ + 6$\hat{j}$) m/s²
    2. (6$\hat{i}$ + 6$\hat{j}$) m/s²
    3. (12$\hat{i}$ + 3$\hat{j}$) m/s²
    4. (3$\hat{i}$ + 6$\hat{j}$) m/s²
  6. An object’s velocity vector changes from $\vec{v_1} = (5\hat{i} - 2\hat{j})$ m/s to $\vec{v_2} = (2\hat{i} + 3\hat{j})$ m/s in 2 seconds. Calculate the average acceleration vector.
    1. (-1.5$\hat{i}$ + 2.5$\hat{j}$) m/s²
    2. (3.5$\hat{i}$ - 0.5$\hat{j}$) m/s²
    3. (-3$\hat{i}$ + 5$\hat{j}$) m/s²
    4. (7$\hat{i}$ - 1$\hat{j}$) m/s²
  7. An object is moving with a velocity vector $\vec{v}(t) = (4t\hat{i} + 3\hat{j})$ m/s. What is the magnitude of its acceleration vector?
    1. 4 m/s²
    2. 3 m/s²
    3. 5 m/s²
    4. 7 m/s²
Click to see Answers
  1. A
  2. D
  3. A
  4. A
  5. A
  6. A
  7. A

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