A particle is moving along a straight line with uniform acceleration $\overrightarrow{a}$,let its velocity change from$\overrightarrow{u}$ to$\overrightarrow{v}$ in an interval of time t then

Given that a particle moving along straight line

With initial velocity = u

Final velocity = v

Uniform acceleration = a

Time taken = t

Then displacement $$\begin{gathered} s=v_{avg}\times t(for any non uniform motion) \\ \Rightarrow s=\left(\frac{u+v}{2}\right)\times t \therefore v=u+at \\ u=v-at \\ we get s=\frac{\left(u+u+at\right)t}{2} or s=\frac{\left(v+v-at\right)t}{2} \\ \Rightarrow s=ut+\frac{1}{2}a{t}^2 \left(or\right) s=vt-\frac{1}{2}a{t}^2 \\ So we get options a, b, c are true. \end{gathered}$$