Are you looking for a detailed blog on SUVAT equations? If yes, then this blog post is made for you. In this blog post, we’ll explain 5 SUVAT equations derivation with examples to make it easy for you to understand the whole concept. Let’s get started with an introduction to SUVAT:
What are SUVAT Equations?
The SUVAT equations are fundamental in classical mechanics. These derivations provide a mathematical framework to describe and understand the motion of objects moving in a straight line with constant acceleration. It is important to understand these equations for your A-level physics and maths revision. The acronym “SUVAT” represents the five variables these equations connect: S (displacement), U (initial velocity), V (final velocity), A (acceleration), and T (time). These SUVAT equations are essential aspects of physics, making you able to solve motion problems with constant acceleration without using calculus.
Key Symbols for Understanding SUVAT Formulas
To fully understand the SUVAT equation, it is important to know the symbols and units involved. Here’s a table that outlines each variable, its description, and the standard International System of Units (SI) used:
| Variable | Description | SI Unit |
| S | Displacement | Metres (m) |
| U | Initial Velocity | Metres per second (m/s) |
| V | Final Velocity | Metres per second (m/s) |
| A | Acceleration | Metres per second squared (m/s2) |
| T | Time | Seconds (s) |
5 SUVAT Equations with Explanation
Take a look at the following SUVAT Equations A Level:
- V = U + AT: This equation relates the final velocity (V) to the initial velocity (U), acceleration (A), and time (T).
- S = (U + V)/2 * T: This calculates displacement (S) by averaging the initial and final velocities over time (T).
- V² = U² + 2AS: This equation determines the final velocity squared from the initial velocity squared, taking into account acceleration and displacement.
- S = UT + 1/2 AT²: This equation computes displacement based on initial velocity, time, and acceleration.
- S = VT – 1/2 AT²: A variation of the previous one, this formula calculates displacement using final velocity, time, and acceleration.
Understanding SUVAT Equations with Examples
Example 1: A particle starts moving from the origin with a speed of 4 m/s along the x-axis and decelerates at a constant rate of 2 m/s². Find the times when the particle reaches the point where x = 3.
First, identify the SUVAT variables:
- Displacement from the origin, S = 3
- Initial speed, U = 4
- Final velocity, V, is not given and not needed
- Acceleration, A = -2 (since it’s deceleration)
- Time, T, is what we need to find
We also note that the units are consistent. The fourth SUVAT equation relates S, U, A, and T:
S=UT+1/2 AT2 => 3= 4T+1/2 * -2*T2
Rearranging and factoring this equation gives:
T2 – 4T+3 = (T-3) (T-1) = 0
This implies T = 1 or T = 3. Therefore, the particle passes the point where x = 3 after 1 second and again after 3 seconds. This happens because the particle starts with a positive speed and decelerates, eventually slowing down to 0, reversing direction, and heading back towards the origin.
Example 2: A dedicated stargazer spots what he believes to be a UFO in the night sky. He measures the object’s speed at 550 m/s and notes that it travels 2 km in approximately 5 seconds after he first sees it. Assuming the object is moving with constant acceleration in a straight line, estimate its acceleration.
Summarizing the information and ensuring the units are consistent:
- S= 2000
- U (not needed)
- V= 550
- A=?
- T=5
The final SUVAT equation relates S, V, A, and T.
S= VT – ½ AT2 => 2000 = 550* 5 – ½ A* 52
Rearranging this equation gives:
A = 2000 – 2750/-1/2* 25 = 60
Therefore, the UFO has an acceleration of 60 m/s².
Conclusion
The blog outlines SUVAT formulas with examples. If you want more clarification, you can contact Bright Mind Tutors.
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