Question

When the object travelled a distance 'S' in time 't' under uniform motion then the
equation to find out 'S' is
(a) S= ut+kat?
(b) u+ Wat
(c) S= ut + lat​

Answer 1

Answer:

Diagrammatic representation of motion is shown below. distance travelled is equal to the sum of the area of rectangle OACD and area of triangle BCD.

Also, slope of DB = BC/DC acceleration

Or a = BC/DC

⇒BC=a(DC)=at

Total area =OA×OD+21×BC×DC

But DC=OA=t

∴s=ut+21×at×t

or s=ut+21×at2

Answer 2

To find:

Equation to find distance S in time t with uniform acceleration ?

Calculation:

We can use Calculus to solve this problem :

$\therefore \: a = k$

$\implies \: \dfrac{dv}{dt} = k$

$\displaystyle\implies \: \int dv = k \: \int \: dt$

$\displaystyle\implies \: v - u = kt$

$\displaystyle\implies \: v =u + kt$

$\displaystyle\implies \: \dfrac{dx}{dt} =u + kt$

$\displaystyle\implies \: \int dx = \int(u + kt )\: dt$

$\displaystyle\implies \: x = ut + \dfrac{1}{2} k {t}^{2}$

$\displaystyle\implies \: S = ut + \dfrac{1}{2} k {t}^{2}$

Hence proved !