A go-kart's velocity changes by 5 m/s during each second. What is the go-kart's acceleration?
Here is a car waiting at a red light. The light turns green. The driver presses the accelerator, and the speedometer starts to climb: 25 mph, 30 mph, 35 mph… The climb follows a rule — one exact enough to tell you what the dial will read five seconds from now, and how much distance the car covers in that time.
There is a set of equations for exactly this kind of motion. They describe it, explain it, and predict what the object will do next. That is what this part of the course looks at.
They're known as the 'kinematic equations', and they work for any object as long as its speed is changing at a constant rate — or, in other words, as long as it has a constant acceleration.
Watch the dial: the same 5 mph gained every second, every second.
That steady gain is a constant acceleration — the one condition the kinematic equations ask for.
One thing to remember: the kinematic equations only work when the acceleration is constant. They do not work if the acceleration is changing.
The same car in stop-and-go traffic: the change is different every second. No single acceleration value covers the trip.
Which motion can the kinematic equations be used to solve?
A subway train speeds up, but its acceleration shrinks as it goes. Can the kinematic equations cover this motion as a whole?
And constant includes zero: a car holding one steady velocity has a constant acceleration of 0 m/s², so the kinematic equations still apply to it.
A car holding a steady 15 m/s gains 0 m/s each second. Its acceleration is constant at zero.
Now consider a train departing a platform, its acceleration holding one steady value the whole time. The acceleration is constant for the whole stretch, so the kinematic equations apply to the motion as a whole.
Now consider a bumper car: it lurches forward, jolts sideways off a collision, and lurches again. The acceleration changes with every lurch and jolt. The kinematic equations hold only while the acceleration is constant, so they do not cover the ride as a whole.
One test decides: does the acceleration hold a single value for the whole motion?
Your turn
A delivery van accelerates steadily away from a stop sign, then holds a steady velocity, then brakes steadily. A student writes one kinematic equation to cover the entire trip. Why is that wrong?
Which motion can the kinematic equations cover as a whole?
A car holds a steady 12 m/s for an entire trip, so its acceleration is 0 m/s² throughout. Can the kinematic equations cover this trip?