Question

how is h= -ut + 1/2 gt^2​

Answer 1

Need to Do :-

• How can we say that h = -ut+½at² .

$\red{\frak{Given}}\Bigg\{ \sf h = -ut + \dfrac{1}{2}gt^2$

We know that the second equation of motion , which establishes the relationship between Displacement , initial Velocity , time and acceleration is :-

• Second equation of motion :-

$\sf\to\red{ s = ut + \dfrac{1}{2}at^2 }$

This is valid for straight line motion , but when a object is projected vertically ( at 90° ) , then here , the

Displacement becomes Height .

Accelⁿ becomes gravity .

Also here we see that , the

• g acts vertically downwards .
• Initial velocity is in upwards dirⁿ .

Now , if we take downwards direction as positive , then the acceleration due to gravity will be positive ( since it a acts downwards ) and the initial velocity will be negative ( since its direction is upwards ) . Henceforth , by sign convention the equation transforms into ,

$\qquad\orange{\underbrace{\boxed{\boxed{\pink{\frak{ h = -ut + \dfrac{1}{2}gt^2 }}}}}}$