Question

Derive 2nd equation of motion by graphical method for 9th standard

Answer 1

equation of position time relationship.
distance travelled. = area of trapezium.
s = 1/2 OC ( O A + B c) .
s = 1/2 t ( u+v ) from equation (1). ( v=u+at)
s = 1/2 t ( u+u + at )
s = 1/2 t ( 2u+ at )
s = 1/2× 2 ut + 1/2 at^2
s = ut+ 1/2at^2
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Answer 2

Equation for position time relation
Initial velocity (u) = OA
final velocity (v) = BC
Time (t) = AD or OC
Distance travelled = Area of trapezium OABC
= 1/2 OC (OA +BC )
S = 1/2 t ( u +v)
from (1) equation v=u+at
S = 1/2 t ( u+ u+ at )
S = 1/ 2 t ( 2u + at )
S = 1/2 t × 2u + 1/2 t × at
S = ut + 1/2 at ^2

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