Linear motion with constant acceleration
Another special type of motion is when the particle travels in a straight line with varying velocity but constant acceleration. We call this type of motion linear motion with constant acceleration.
Position, velocity and acceleration in linear motion with constant acceleration
- position: \(x(t) = x_0 + v_{x0} t + \frac{a_x}{2} t^2,\) wherein \(v_{x0}\) indicates the initial velocity
- velocity: \(v_x = v_{x0} + a_x t\)
- acceleration: \(a_x = \mathrm{const}\)
Alternative formula for the displacement
Many times we are not interested in the time it takes to reach a certain velocity. Consider, for example, the task of determining the stopping distance for a lorry that can brake with a constant acceleration. We could determine the time it takes for the lorry to stop and from that the stopping distance, but it is more convenient to have a direct formula.
When we wish to eliminate the time interval, we can use the formula
\[2 a_x \Delta x = v_x^2 - v_{x0}^2.\]