Question

v=u+at is used in case of variable acceleration. Comment

Answer 1

Explanation:

There are four variables which put together in an equation can describe this motion. These are Initial Velocity (u); Final Velocity (v), Acceleration (a), Distance Traveled (s) and Time elapsed (t). The equations which tell us the relationship between these variables are as given below.

v = u + at

v2 = u2 + 2as

s = ut + 1/2 at2

average velocity = (v + u)/2

Of course, these equations are applicable only if acceleration is constant

Armed with these equations you can do wonderful things like calculating a cars acceleration from zero to whatever in 60 seconds !!

Answer 2

To check this out, let's consider the math behind it and you can find out!

According to the question,

a = function of time = f(t)

Acceleration is defined as the rate of change of velocity;

a = dv/dt = f(t)

Integrating both sides;

v = k + {integral of f(t) wrt time}

If f(t)=constant= a, then

=> integral of f(t) wrt time = a*t

Hence, the equation would be:

v = k + at which is equivalent to v = u +at

This is acceptable with uniform acceleration as it is constant.

But let's assume f(t) = x*t

=> integral of f(t) wrt time = x*(t^2)/2

So, equation is: v = k + x*(t^2)/2

Which will not be as the equation v = u + at