Question

How will the equations of motion change for an object moving with a uniform velocity change?

Answer 1

Equations of motion are given by:

$$\begin{gathered} v=u+at \\ {v}^2=u^2+2as \\ s=ut+\frac{1}{2}a{t}^2 \end{gathered}$$

Where,

u and v are the initial and final velocities respectively, a is acceleration, t is time, and s is a distance traveled.

Equation of motion change for an object moving with a uniform velocity:

When there is a uniform change in velocity initial and final velocities are the same therefore $v=u$.

Applying $v=u$ in the equations of motion.

$$\begin{gathered} v=u+at \\ \Rightarrow at=0 \\ \Rightarrow a=0; \\ \mathrm{And}, \\ {v}^2=u^2+2as \\ \Rightarrow v^2-u^2=2as \\ \Rightarrow 2as=0; \\ \mathrm{And}, \\ s=ut+\frac{1}{2}a{t}^2 \\ \Rightarrow s=ut \end{gathered}$$

Hence, at uniform velocity, acceleration is zero, and distance traveled is equal to the product of speed and time.