**Equations of Uniformly Accelerated Motion:**

If a body starts with velocity (u) and after time t its velocity changes to v, if the uniform acceleration is a and the distance travelled in time t is s, then the following relations are obtained, which are called equations of uniformly accelerated motion.

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## Uniformly Accelerated Motion | Definition, Equations – Motion in a Straight Line

**Uniformly Accelerated Motion Equations:**

(i) v = u + at

(ii) s = ut + \(\frac{1}{2}\) at²

(iii) v² = u² + 2as

(iv) Distance travelled in rath second.

s_{n} = u + \(\frac{a}{2}\) (2n -1)

If a body moves with uniform acceleration and velocity changes from u to v in a time interval, then the velocity at the mid-point of its path

= \(\frac{\sqrt{u^{2}+v^{2}}}{2}\)

**Non-Uniformly Accelerated Motion Definition:**

When acceleration of particle is not constant then motion is called non-uniformlly accelerated motion.

For one dimensional motion,

where, Δs is displacement in time Δt, Δv is velocity in time Δt and a is instantaneous acceleration.

In component form,

\(\mathbf{a}=a_{x} \cdot \hat{\mathbf{i}}+a_{y} \cdot \hat{\mathbf{j}}+a_{z} \cdot \hat{\mathbf{k}}\)

where, a_{x} = \(\frac{d v_{x}}{d t}\), a_{y} = \(\frac{d v_{y}}{d t}\) and a_{z} = \(\frac{d v_{z}}{d t}\)

**Motion in a Straight Line Topics:**