Edexcel IGCSE Physics · Spec 1.10, 1.13
The No-Time Kinematics Equation and Vectors
Covers use v squared = u squared + 2as, Rearrange the equation and Distinguish scalar and vector quantities.
Physics revision video
The No-Time Kinematics Equation and Vectors
Prefer to watch on YouTube? Open this video on YouTube.
Explained
The equation with no time in it, and why vectors need a direction
The equation is v squared equals u squared plus 2 a s. Final velocity squared equals initial velocity squared plus twice the acceleration times the distance.
Its whole purpose is that time does not appear. Every other equation of motion contains a time, so if a question gives you an initial velocity, an acceleration and a distance, and asks for a final velocity, this is the one that fits without needing to find the time first.
Recognising when to use it
List what the question gives you and what it asks for. If those four quantities are velocities, acceleration and distance, with no time mentioned anywhere, use this equation.
If a time is given or wanted, one of the other equations is quicker. You can still reach the answer by finding the time first and using two equations, and that route earns full marks, but it is longer and gives the arithmetic two chances to go wrong.
Rearranging it
For the distance, s equals v squared minus u squared, all divided by 2 a.
For the acceleration, a equals v squared minus u squared, all divided by 2 s.
For the initial velocity, u squared equals v squared minus 2 a s, and then take the square root.
The square root is the step people forget. Calculating v squared and writing that number down as the answer is the standard error in this topic, and the number is usually large enough to look wrong if you pause to consider whether it is a sensible speed.
Two starting values simplify things when they appear. If the object starts from rest, u is zero and the first term vanishes. If it comes to a stop, v is zero and the equation becomes u squared equals minus 2 a s, which is why the acceleration comes out negative for anything braking.
Signs
Choose a positive direction before you write anything down, and keep it for the whole question.
Deceleration is a negative acceleration when the object is moving in the positive direction. An object thrown upwards has a positive initial velocity and an acceleration of minus 10 metres per second squared, because gravity acts downwards.
Because velocities appear squared, the sign of u and v disappears from the arithmetic, which is convenient. The signs of a and s still matter, and getting them inconsistent is what produces a negative value under a square root.
What the mark scheme accepts and rejects
An Edexcel International GCSE Physics mark scheme splits a question using this equation into three marks: the substitution, the rearrangement, and the evaluation. Its notes allow the substitution and the rearrangement in either order, and allow an error carried forward from the previous part.
Two further notes are worth having. It says to ignore the sign, so a negative distance or a negative acceleration is not penalised in the final answer. And a power of ten error costs one mark rather than the question.
It also states that a correct answer without working scores all the marks. That is not an invitation to skip the working, because the reverse is what matters: working without a correct answer still scores two of the three, and an unsupported wrong answer scores none.
Elsewhere the same paper offers this equation as an alternative route. On a question asking for a distance from a velocity time graph, the expected method is the area under the line, and the notes allow alternative valid methods, giving the use of v squared equals u squared plus 2 a s with a calculated acceleration as the example. On another, asking for a height, it allows this equation for full marks in place of the energy method.
So the mark schemes are consistently indifferent to which correct route you take. What they are not indifferent to is whether the route is visible.
Scalars and vectors
A scalar has size only. A vector has both size and direction.
Distance, speed, mass, time, energy and temperature are scalars. Displacement, velocity, acceleration, force, weight and momentum are vectors.
The pairs are the point. Distance is how far you travelled; displacement is how far you ended up from where you started, and in which direction. Speed is how fast; velocity is how fast and which way. Walk a full lap of a track and your distance is the length of the lap while your displacement is zero.
This matters for the equation above because s, u, v and a are all vectors, which is why a direction has to be chosen before the numbers go in.
Vectors in the same straight line are added by giving one direction a positive sign and the other a negative one. At right angles they are combined with Pythagoras, and the direction is found from the angle. Scalars are simply added.
Spec 1.10, 1.13
What you need to know
- Use v squared = u squared + 2as
- Rearrange the equation
- Distinguish scalar and vector quantities
Active recall
Quick check
Answer each question before opening the answer.
When is v2 = u2 + 2as useful?
For constant acceleration when time is absent
Is momentum scalar or vector?
Vector
What is the final step after calculating v squared?
Take the appropriate square root
Physics revision app
Take this topic further in the app
275 guided topics with questions marked as you answer them, section checkpoints and timed practice papers. Fifteen topics are free to try, with no card needed.