Using suvat (AQA A-Level Mathematics): Revision Notes

Each letter in SUVAT represents a different physical quantity:

• S: Displacement (in metres, $m$ )
• U: Initial velocity (in metres per second, $m/s$ )
• V: Final velocity (in metres per second, $m/s$ )
• A: Acceleration (in metres per second squared, $m/s^2$ )
• T: Time (in seconds, $s$ )

1. v = u + at

• Description: Final velocity after time $t$ with initial velocity $u$ and constant acceleration $a$ .
• Use: When you need to find final velocity or time.

2. $s = ut + \frac{1}{2}at^2$

• Description: Displacement after time $t$ with initial velocity $u$ and constant acceleration $a$ .
• Use: When you need to find displacement.

3. $s = vt - \frac{1}{2}at^2$

• Description: Displacement after time $t$ with final velocity $v$ and constant acceleration $a$ .
• Use: When you have final velocity and time and need to find displacement.

4. $s = \frac{u + v}{2} \times t$

• Description: Displacement when you know both the initial and final velocities over a period of time $t$.
• Use: When you need to find displacement without knowing acceleration.

5. $v^2 = u^2 + 2as$

• Description: Final velocity squared when you know initial velocity, acceleration, and displacement.
• Use: When you need to find final velocity or displacement without involving time.

To effectively use the SUVAT equations, follow these steps: 6. Identify Known and Unknown Quantities:

• Write down what is given in the problem (e.g., initial velocity $u$ , time $t$ , etc.).
• Identify which quantity you need to find (e.g., final velocity $v$ ).

7. Choose the Appropriate Equation:

• Select the SUVAT equation that includes the known quantities and the one you need to find.
• Ensure that you have at least three known variables to solve for the unknown.

8. Solve the Equation:

• Substitute the known values into the equation.
• Rearrange the equation if necessary to solve for the unknown quantity.

9. Check Units and Reasonableness:

• Ensure all quantities are in consistent units (e.g., metres, seconds).
• Check if the result makes sense in the context of the problem.

Example 1: A car accelerates from rest at $2 \, m/s^2$ for $5$ seconds. What is its final velocity?

• Given: $u = 0 \, m/s$ (from rest), $a = 2 \, m/s^2$ , $t = 5 \, s$
• To Find: Final velocity $v$ Using $v = u + at$ :

$v = 0 + (2)(5) = 10 \, m/s$

The final velocity is 10 m/s .

Example 2: A ball is thrown upwards with an initial velocity of $15 \, m/s$ . Find the maximum height it reaches.

• Given: $u = 15 \, m/s$ , $v = 0 \, m/s$ (at maximum height), $a = -9.8 \, m/s^2$ (gravity, acting downwards)
• To Find: Displacement $s$ (maximum height) Using $v^2 = u^2 + 2as$ :

$0 = (15)^2 + 2(-9.8)s$

$0 = 225 - 19.6s$

$19.6s = 225$

$s = \frac{225}{19.6} \approx 11.48 \, m$

The maximum height reached is approximately 11.48 m .

• Consistent Sign Convention: Choose a direction as positive (usually upwards or forwards) and stick to it throughout the problem.
• Use Gravity Correctly: When dealing with vertical motion, remember that the acceleration due to gravity is -9.8 m/s² (downwards).
• Recognise When to Use Each Equation: Understand which SUVAT equation is best for the given situation, based on what you know and what you need to find.