Question

What do you mean by uniform and non-uniform acceleration? Explain with example

Answer 1

I hope this will help you

Answer 2

Answer:

Explanation:

Uniform acceleration is constant acceleration.

Acceleration is the change of velocity in unit time.

$a = \frac{\Delta v}{\Delta t}$

Suppose, the velocity at t = 1 sec is 10 m/s. Then at t = 2 secs, the velocity is 20 m/s. Similarly, at t = 3 secs, the velocity will be 30 m/s. From this, we can deduce that,

$velocity = 10 \times time\\v = 10 \times t$

This is linear equation. We can plot it on the graph as a straight line ( attched with the answer ). From the above equation,

$\frac{v}{t} = a = 10 \ m/s^2$

We can verify this too.

$\frac{10 \ m/s}{1 \ t} = \frac{20 \ m/s}{2 \ t} = \frac{30 \ m/s}{3 \ t} = 10 \ m/s^2$

Hence, the ratio of velocity upon time ( acceleration ) remains constant for any value of v and t. Hence, it is uniform and constant.

Non-Uniform acceleration.

In this case, the ratio which we discussed earlier is not constant. Hence, the graph of velocity-time is not a straight line ( attched with the answer ).

Suppose, for time ( t ),

when t = 1 sec, v = 10 m/s.

when t = 2 sec, v = 15 m/s.

when t = 3 sec, v =25 m/s.

If we calculate the acceleration or the ratios of velocity to time,

$\frac{10 \ m/s}{1 \ t} \neq \frac{15 \ m/s}{2 \ t} \neq \frac{25 \ m/s}{3 \ t} \neq 10 \ m/s^2$

Hence, the ratio is not constant and hence it is termed as non-uniform acceleration. Also, for non-uniform acceleration, the formula changes to,

$a =  \lim_{ \Delta t \to 0}  \frac{\Delta v}{\Delta t}$