Constant Acceleration Quiz with Answers: Test Your Understanding

📚 Quick Study Guide

• 📏 Displacement: When acceleration is constant, displacement ($\Delta x$) can be calculated as: $\Delta x = v_0t + \frac{1}{2}at^2$, where $v_0$ is the initial velocity, $t$ is time, and $a$ is acceleration.
• ⏱️ Final Velocity: The final velocity ($v$) after a time $t$ is: $v = v_0 + at$.
• 🚀 Velocity-Displacement Relation: A useful formula relating final velocity, initial velocity, acceleration, and displacement is: $v^2 = v_0^2 + 2a\Delta x$.
• 💡 Average Velocity: When acceleration is constant, the average velocity is: $v_{avg} = \frac{v_0 + v}{2}$. This is helpful for calculating displacement: $\Delta x = v_{avg} t$.
• 🍎 Free Fall: An object in free fall experiences constant acceleration due to gravity, approximately $g = 9.8 m/s^2$. The sign of $g$ depends on the coordinate system chosen.

🧪 Practice Quiz

1. A car accelerates from rest at a constant rate of $3 m/s^2$ for 4 seconds. What is the final velocity of the car?
   1. 6 m/s
   2. 9 m/s
   3. 12 m/s
   4. 15 m/s
2. An object is thrown upwards with an initial velocity of $10 m/s$. Assuming constant acceleration due to gravity ($g = 9.8 m/s^2$), what is the maximum height reached by the object?
   1. 2.55 m
   2. 5.10 m
   3. 10.2 m
   4. 20.4 m
3. A ball rolls down an incline with a constant acceleration of $2 m/s^2$. If it starts from rest, how far does it travel in 3 seconds?
   1. 3 m
   2. 6 m
   3. 9 m
   4. 12 m
4. A rocket accelerates from $20 m/s$ to $80 m/s$ over a distance of $200 m$. What is the rocket's acceleration, assuming it is constant?
   1. $10 m/s^2$
   2. $15 m/s^2$
   3. $20 m/s^2$
   4. $25 m/s^2$
5. A cyclist starts from rest and accelerates at a constant rate of $0.5 m/s^2$. How long will it take for the cyclist to reach a speed of $15 m/s$?
   1. 15 s
   2. 20 s
   3. 25 s
   4. 30 s
6. An airplane needs to reach a speed of $280 km/h$ on the runway for takeoff. If the runway is $1000 m$ long, what should be the minimum constant acceleration of the plane?
   1. $1.08 m/s^2$
   2. $2.17 m/s^2$
   3. $3.26 m/s^2$
   4. $4.35 m/s^2$
7. A car is moving with a velocity of $10 m/s$ and accelerates uniformly at a rate of $2 m/s^2$. What will its velocity be after traveling a distance of 50 m?
   1. $10 \sqrt{2} m/s$
   2. $10 m/s$
   3. $15 m/s$
   4. $20 m/s$