Examples of one-dimensional kinematics problems with solutions

📚 Quick Study Guide

• 📏 Displacement: Change in position ($\Delta x = x_f - x_i$).
• ⏱️ Velocity: Rate of change of displacement ($v = \frac{\Delta x}{\Delta t}$). Average velocity is total displacement divided by total time.
• acceleration 🏎️ Acceleration: Rate of change of velocity ($a = \frac{\Delta v}{\Delta t}$).
• ✨ Kinematic Equations (Constant Acceleration):
  • $v_f = v_i + at$
  • $\Delta x = v_i t + \frac{1}{2} a t^2$
  • $v_f^2 = v_i^2 + 2 a \Delta x$
  • $\Delta x = \frac{1}{2}(v_i + v_f)t$
• 💡 Problem-Solving Tips:
  • Read the problem carefully.
  • Identify knowns and unknowns.
  • Choose the appropriate kinematic equation.
  • Solve for the unknown.
  • Check your answer (units, sign, magnitude).

Practice Quiz

1. A car accelerates from rest to 20 m/s in 5 seconds. What is its acceleration?
   1. 2 m/s²
   2. 3 m/s²
   3. 4 m/s²
   4. 5 m/s²
2. A ball is thrown vertically upwards with an initial velocity of 15 m/s. What is the maximum height it reaches? (Assume g = 9.8 m/s²)
   1. 8.62 m
   2. 11.48 m
   3. 22.96 m
   4. 34.44 m
3. A cyclist travels 100 meters in 10 seconds at a constant velocity. What is the cyclist's velocity?
   1. 5 m/s
   2. 10 m/s
   3. 15 m/s
   4. 20 m/s
4. An object starts from rest and accelerates at 3 m/s² for 4 seconds. How far does it travel?
   1. 12 m
   2. 18 m
   3. 24 m
   4. 30 m
5. A train moving at 30 m/s applies brakes and decelerates at a rate of -2 m/s². How long does it take to come to a complete stop?
   1. 10 s
   2. 12 s
   3. 15 s
   4. 18 s
6. A stone is dropped from a bridge. If it takes 3 seconds to hit the water, how high is the bridge? (Assume g = 9.8 m/s²)
   1. 29.4 m
   2. 44.1 m
   3. 58.8 m
   4. 88.2 m
7. A runner accelerates from 2 m/s to 6 m/s over a distance of 8 meters. What is the runner's acceleration?
   1. 1 m/s²
   2. 2 m/s²
   3. 3 m/s²
   4. 4 m/s²