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Answers
When we are talking about motion in a straight line with constant acceleration, there are three equations of motion, which are helpful in determining one of the unknown parameters:
v = u+ at
x = ut + 1/2 at²
v² = u² + 2as
where,
v = final velocity of the particle
u = initial velocity of the particle
s = displacement of the particle
a = acceleration of the particle
t = time interval in which the particle is in consideration
A simple algebraic method, graphical method and calculus method are the ways to derive equation of motion.
Remember, the sign convention is to be maintained while applying these equations. One direction is considered to be positive and another one as negative. One of the common examples of uniformly accelerated motion is freely falling bodies. The only acceleration which is acting on the body is g (acceleration due to gravity). If we are taking the vertically upward direction as the positive, the acceleration due to gravity (g) will be negative since it is in the downward direction.
If an object's speed (velocity) is increasing at a constant rate then we say it has uniform acceleration. The rate of acceleration is constant. If a car speeds up then slows down then speeds up it doesn't have uniform acceleration.