Solved Examples of Acceleration Problems in Physics

📚 Quick Study Guide

• ⏱️ Acceleration is the rate of change of velocity with respect to time.
• 📏 The standard unit for acceleration is meters per second squared ($m/s^2$).
• 📐 Formula for average acceleration: $a = \frac{\Delta v}{\Delta t} = \frac{v_f - v_i}{t_f - t_i}$, where $v_f$ is the final velocity, $v_i$ is the initial velocity, $t_f$ is the final time, and $t_i$ is the initial time.
• 🚗 Constant acceleration means the velocity changes at a steady rate.
• 💡 If acceleration is in the same direction as velocity, the object speeds up. If it's in the opposite direction, the object slows down.
• 🍎 Acceleration due to gravity (g) is approximately $9.8 m/s^2$ near the Earth's surface.
• 📝 Equations of motion (kinematics) for constant acceleration:
  • $v_f = v_i + at$
  • $\Delta x = v_i t + \frac{1}{2} a t^2$
  • $v_f^2 = v_i^2 + 2 a \Delta x$

Practice Quiz

1. Question 1: A car accelerates from rest to 20 m/s in 5 seconds. What is its average acceleration?
   1. 2 $m/s^2$
   2. 4 $m/s^2$
   3. 5 $m/s^2$
   4. 10 $m/s^2$
2. Question 2: An object is thrown upwards with an initial velocity of 15 m/s. What is its acceleration at the highest point (ignoring air resistance)?
   1. 0 $m/s^2$
   2. 9.8 $m/s^2$ downwards
   3. 9.8 $m/s^2$ upwards
   4. -15 $m/s^2$
3. Question 3: A ball rolls down a ramp with a constant acceleration of 2 $m/s^2$. If it starts from rest, how far will it travel in 3 seconds?
   1. 6 meters
   2. 9 meters
   3. 12 meters
   4. 18 meters
4. Question 4: A train slows down from 30 m/s to 10 m/s in 20 seconds. What is its acceleration?
   1. -1 $m/s^2$
   2. 1 $m/s^2$
   3. 1.5 $m/s^2$
   4. -1.5 $m/s^2$
5. Question 5: A rocket accelerates at a rate of 50 $m/s^2$ for 5 seconds. If its initial velocity is 100 m/s, what is its final velocity?
   1. 150 m/s
   2. 250 m/s
   3. 300 m/s
   4. 350 m/s
6. Question 6: A car traveling at 25 m/s applies the brakes and comes to a stop in 5 seconds. What is the distance it covers while braking?
   1. 62.5 meters
   2. 125 meters
   3. 150 meters
   4. 250 meters
7. Question 7: An object accelerates from 10 m/s to 30 m/s over a distance of 40 meters. What is its acceleration?
   1. 2.5 $m/s^2$
   2. 5 $m/s^2$
   3. 7.5 $m/s^2$
   4. 10 $m/s^2$