A ball rolls from rest down a smooth ramp that is 16.0m long. The acceleration of the ball is constant at 40ms^2.
A) how long does the ball take to roll the first 4.0m?
B) what is the speed of the ball when it is halfway down the ramp? (how far it has travelled)
C) how long does the ball take to travel the final 8.0m?
d = (1/2) a t^2 = 20 t^2
4 = 20 t^2
t^2 = .2
t = 0.447 seconds
8 = 20 t^2
t^2 = 0.4
t = .632
v = a t = 40 ( .632) = 16 m/s
which question is that for
A or C?
What is the final speed of the ball?
Vi at 8 m = 16
now accelerates at 40 m/s^2 for 8 more meters
v = Vi + a t = 16 + 40 t
x = Xi + Vi t +20 t^2
16 = 8 + 16 t + 20 t^2
20 t^2 + 16 t - 8 = 0
5 t^2 + 4 t - 2 = 0
t = .348 seconds
Hey, it takes awhile :)
by the way
https://www.mathsisfun.com/quadratic-equation-solver.html
They did not ask for final speed but I gave you the recipe:
v = Vi + a t = 16 + 40 t
= 16 + 40 ( .348)