Question

If an object moves at a non-zero constant acceleration for a certain interval of time, then the distance it covers in that time depends on

Answer 1

1.we know,

$s = ut + 1 \div 2 \times at {2}$

2.Thus the distance will depend on the initial velocity u, the time interval t, and the accelaration a.

Answer 2

Given:

Non zero acceleration a

To find:

Distance covered s

Solution:

It is given that the acceleration of a body = a

we know that

$a \: = \: \frac{ d v}{ d t} \: = \: constant$

On integrating both sides with respect to time

$\int a \delta \: t \: = \: at \: = v| ^{v} _ u$

So

v - u = at

As v = final velocity

u = initial velocity

And

v = u + at

As we know that

$v \: = \: \frac{ds}{dt}$

On integrating above equation with respect to t.

$\int \: ds\: = \: \int \: (u \: + at)dt$

So

The distance covered =

$\bf \: s \: = \: ut \: + \: \frac{1}{2} at ^{2}$