Question

{s=ut+1/2at*t} derive the equation

Answer 1

Answer:Let the distance be “s”. We know that

Distance = Average velocity × Time. Also, Average velocity = (u+v)/2

Therefore, Distance (s) = (u+v)/2 × t

Also, from v = u + at, we have:

s = (u+u+at)/2 × t = (2u+at)/2 × t

s = (2ut+at²)/2 = 2ut/2 + at²/2

or s = ut +½ at²

Explanation: Hope it helps

Answer 2

Answer:

The given equation (s = ut+ 1/2 at²) can be proven by using 2 methods: the graphical method and the algebraic method.

Explanation:

Method - 1: Graphical method

Here is a graph that shall prove it:

Displacement (s) = area under the curve

=> Area of rectangle + Area of triangle

=> AE*OE + 1/2( AB*AD)

=> AE*OE + 1/2( AB*OE)

=> ut + 1/2 t* (v-u)

=> ut + 1/2 at*t

=> ut + 1/2 at²

Method - 2: Algebraic method

Displacement (s) = Avg. velocity * time

=> {(v+u)/2} * t

=>{(u + at +u)/2} * t

=>{( 2u + at)/2} * t

=> (u + 1/2 at) * t

=> ut + 1/2 at²

Hence, proved

(Sorry that I couldn't display the graph for the first proof).