Solving Problems with Kinematic Equations

Solving problems with kinematic equations can be broken down into simple steps

Step 1: Write out the variables that are given in the question, both known and unknown, and use the context of the question to deduce any quantities that aren’t explicitly given
- e.g. for vertical motion a = ± 9.81 m s^–2, an object which starts or finishes at rest will have u = 0 or v = 0
Step 2: Choose the equation which contains the quantities you have listed
- e.g. the equation that links s, u, a and t is s = ut + ½at²
Step 3: Convert any units to SI units and then insert the quantities into the equation and rearrange algebraically to determine the answer

Worked example

The diagram shows an arrangement to stop trains that are travelling too fast.

SUVAT Problems Worked Example (1), downloadable AS & A Level Physics revision notes

Trains coming from the left travel at a speed of 50 ms^-1.

At marker 1, the driver must apply the brakes so that the train decelerates uniformly in order to pass marker 2 at no more than 10 ms^-1. The train carries a detector that notes the times when the train passes each marker and will apply an emergency brake if the time between passing marker 1 and marker 2 is less than 20 s.

How far from marker 2 should marker 1 be placed?

Answer:
Step 1: List the known quantities

u = 50 m s^–1
v = 10 m s^–1
t = 20 s
s = ?

Step 2: State the appropriate equation

The equation that links u, v, t and s are:

$s = \frac{(u + v)}{2} t$

Step 3: Substitute in the values

$s = \frac{(50 + 10)}{2} \times 20 = 600 m$

Exam Tip

This is arguably the most important section of this topic, you can always be sure there will be one, or more, questions in the exam about solving problems with the kinematic equations. Make sure you've correctly selected the final and initial velocity.

Solving Problems with Kinematic Equations (CIE A Level Physics)

Revision Note