Which equation do I use?

The idea

The kinematic equations relate s, t, u, v and a and predict future position or velocity, but hold only for constant acceleration; in straight-line motion in both directions, the signs of u, v, a and s give their directions.

A car at a traffic light

A car waits at a light and then speeds up. We know some of its numbers and want to find another one.

What must be true about the acceleration for the equations we learnt to work?

• It must be constant
• It changes every second
• It must be zero

Match the equations

Tap a description on the left, then the equation it belongs to.

A set of tools

Each equation links four of the five quantities s, t, u, v and a, and leaves one out. Choose the equation that leaves out the quantity you neither know nor need. They work only when the acceleration is constant.

The kinematic equations relate s, t, u, v and a and can predict the position or velocity of the object at a future time. They hold only for constant acceleration. For straight-line motion in both directions, the signs of u, v, a and s give their directions.

Notes

The equations relate s, t, u, v and a and hold only for constant acceleration. The signs of u, v, a and s show their directions.

Check yourself

When are the kinematic equations valid?

In straight-line motion in both directions, what do the signs of u, v, a and s tell us?

What can the kinematic equations be used to predict?

A car starts from rest and has a constant acceleration of 2 m s⁻². After moving 25 m, what is its velocity? (Use the equation without time.)

Answer: 10 m s⁻¹

v² = 0 + 2 × 2 × 25 = 100, so v = 10 m s⁻¹.

• For any motion, even when the acceleration keeps changing. The equations were derived for constant acceleration. They do not hold when it changes.
• Only when the acceleration is constant — correct. Yes!
• Only when the object is at rest. The equations are for motion with constant acceleration. They are not limited to an object at rest.
• The size of each quantity. The size is given by the number. The sign gives the direction.
• The time at which each occurs. The signs have nothing to do with time. They show directions.
• The direction of each of those quantities — correct. Yes!
• The position or velocity of an object at a future time — correct. Yes!
• The colour of the object. The equations relate s, t, u, v and a. They say nothing about colour.
• The route of the object on a map. The equations give position and velocity along the line of motion, not a route on a map.