Solved Examples: Applying Δx = v₀t + (1/2)at² to Physics Problems

📚 Quick Study Guide

• 📏 Displacement (Δx): The change in position of an object. Measured in meters (m).
• ⏱️ Initial Velocity (v₀): The velocity of the object at the beginning of the time interval. Measured in meters per second (m/s).
• ⏳ Time (t): The duration of the motion. Measured in seconds (s).
• acceleration (a): The rate of change of velocity. Measured in meters per second squared (m/s²).
• 🍎 The Formula: $\Delta x = v_0t + \frac{1}{2}at^2$ This equation calculates displacement when initial velocity, time, and acceleration are known and constant.
• ⚠️ Assumptions:** This formula assumes constant acceleration in one dimension. If acceleration changes, or the motion is in multiple dimensions, this formula alone is insufficient.

Practice Quiz

1. A car starts from rest and accelerates at a constant rate of 3 m/s² for 4 seconds. How far does it travel during this time?
   1. A. 12 m
   2. B. 24 m
   3. C. 36 m
   4. D. 48 m
2. An object is thrown vertically upwards with an initial velocity of 15 m/s. Assuming negligible air resistance and an acceleration due to gravity of -9.8 m/s², how long will it take to reach its maximum height? (Hint: at max height, final velocity is 0. Use related kinematic equations to first find the time.)
   1. A. 1.53 s
   2. B. 2.0 s
   3. C. 2.5 s
   4. D. 3.0 s
3. A ball rolls down an inclined plane with a constant acceleration of 2.5 m/s². If it starts from rest, what is its displacement after 6 seconds?
   1. A. 15 m
   2. B. 30 m
   3. C. 45 m
   4. D. 50 m
4. A cyclist starts from rest and accelerates at 1.5 m/s² for 8 seconds. What distance does the cyclist cover during this time?
   1. A. 12 m
   2. B. 48 m
   3. C. 64 m
   4. D. 96 m
5. A rocket accelerates from 10 m/s to 50 m/s in 5 seconds with constant acceleration. How far does it travel?
   1. A. 100 m
   2. B. 150 m
   3. C. 200 m
   4. D. 250 m
6. A car traveling at 20 m/s applies the brakes and decelerates at a constant rate of -4 m/s². How far does it travel before coming to a stop?
   1. A. 25 m
   2. B. 50 m
   3. C. 75 m
   4. D. 100 m
7. A train starts from rest and reaches a velocity of 30 m/s in 10 seconds. Assuming constant acceleration, what is the distance covered by the train?
   1. A. 100 m
   2. B. 150 m
   3. C. 200 m
   4. D. 250 m