Question

a paricles speed equation is v=v suffix 0+gt+ft². when t=0 then displacement is equal to 0. after 1 second what is the displacement​

Answer 1

QuesTion :-

A particle's speed equation is v = v₀+gt+ft². When t = 0 then displacement is equal to 0. After 1 second what is the displacement​?

SoluTion :-

$\rm {v=v_{0}+gt+ft^{2}}\\\\\\\\\\\rm {\therefore v=\frac{dx}{dt} = \int\limits^x_0 \, dx =\int\limits^t_0 {v} \, dt }\\\\\\\\\\\rm {x=\int\limits^t_0(v_{0}+gt+ft^{2}) dt}\\\\\\\\\\\rm {x=v_{0}t+\frac{gt^{2}}{2} +\frac{ft^{2}}{3} }$

At t = 1 second

$\sf {\therefore x=v_{0}+\frac{g}{2} +\frac{f}{3} }$