When the position of object changes on a straight line i.e. motion of object along straight line is called motion in one dimension.
One-dimensional motion can be described using formulas that relate displacement, velocity and acceleration. Velocity is the rate of change of displacement with respect to time. Acceleration is the rate of change of velocity with respect to time. In these formulas, the acceleration is assumed to be constant. The unit of displacement is the meter (m), the unit of velocity is meters per second (m/s), and the unit of acceleration is meters per second squared (m/s2).
Velocity
\[final \; velocity =(initial \; velocity)+(acceleration)(time) \]
\[v_{x}=v_{0x}+a_{x}t \]
Displacement
\[final \; displacemet = (initial \; displacement)+(initial\; velcity)(time)+\frac{1}{2}(acceleration(time)^{2}) \]
\[x= x_{0}+v_{0x}t+\frac{1}{2}a_{x}t^{2} \]
Velocity, Acceleration, Displacement
\[(final \; velocity)^{2}= (initial veocity)^2+2(acceleration)(final\; displacement - initial \; displacement) \]
\[ v_x^2 = v_{0x}^2 + 2a_x (x-x_0) \]
Displacement and Velocity
\[final \; displacement - initail \; displacement ) = \left [ \frac{\left ( initial \; velocity \right ) + \left (final \; velocity \right )}{2} \right ] \left (time \right ) \]
\[ x-x_0 = \left ( \frac{v_{0x} +v_x}{2} \right )t \]
x0 = initial displacement (m)
x = final displacement (m)
v0x = initial velocity (m/s)
vx = final velocity (m/s)
ax = acceleration (m/s2)
t = time (s)
let value of X0=X ,v0x= y,vx =x, ax = a
