# A particle is thrown vertically upwards with some initial velocity.The ratio of distance covered by the particle in time t/2 and 3t/2 is??

Arun Kumar IIT Delhi
$x_{t/2}=vt/2-1/2g(t/2)^2 \\=>x(3t/2)=v(3t/2)-1/2g(3t/2)^2 \\ratio=(v(3t/2)-1/2g(3t/2)^2)/(vt/2-1/2g(t/2))^2 \\=>ratio=(12v-g(3t)^2)/(4v-gt^2)$