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.
sn = 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
= \(\frac{\sqrt{u^{2}+v^{2}}}{2}\)
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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, ax = \(\frac{d v_{x}}{d t}\), ay = \(\frac{d v_{y}}{d t}\) and az = \(\frac{d v_{z}}{d t}\)
Motion in a Straight Line Topics: