Question

A roller skater, DJ, starts off with an initial velocity of 3 m/s before he gets to a sloppy surface when he gains speed at a constant rate. If after 8 seconds, he is already moving 7 m/s, find an expression of his speed and distance t seconds after he started gaining speed. given that the length of the slope is 72m, what is his speed at the bottom of the slope? *

Answer 1

v = Vi + a t if a is constant
7 = 3 + a * 8
8 a= 4
a = 1/2 m/s^2
v =Vi + (1/2)t = 3 +t/2
d = Vi t + 1/2 a t^2 = 3 t + t^2 / 4
72 = .25 t^2 + 3 t
solve quadratic for t
then v = 3 + t/2