I keep making a math error but I'm not sure what it is exactly?

Question

The length of the barrel of a primitive blowgun is 1.8 m. Upon leaving the barrel, a dart has a speed of 19 m/s. Assuming that the dart is uniformly accelerated, how long does it take for the dart to travel the length of the barrel?

whats the proper method of working this out?

step by step please! :]

Answer 1

KNOW:

v = 19 m/s = velocity_final

x = 1.8 m = position/distance_final

FIND:

t = time

STARTING OUT EQUATIONS:

v = a*t

x = 0.5*a*t^2

SOLVE FOR a_acceleration

v = a*t  ..........=> a = v/t

x = 0.5*a*t^2...=> a = 2*x/t^2

GET RID OF a_acceleration and solve for t_time

(by setting above a=v/t equal to a=2*x/t^2)

v/t = 2*x/t^2...=> t = 2*x/v

SOLVE PROBLEM

t = 2 * (1.8 m) / (19 m/s)

t = 0.1895 s

There's other ways to do this, like using {v^2 = 2*a*x} before using {v=a*t} to find the time.  The proper method is the one that you like the best.

Answer 2

first, you already have 1/19 second, for the 1m. Then, divide 1/19 by 5 so that for each amount of time that is (1/95 second) is .2 a meter and multiply it by 4 to get .8, which ends up being 4/95 second. Add that original 1/19 (lets make it 5/95 to be easy) to the 4/95 and you get 9/95 of a second to travel the whole barrel.

That might not be the proper method, but that's what I would do.