how long did the dart travel?

Question

The length of the barrel of a primitive blowgun is 1.7 m. Upon leaving the barrel, a dart has a speed of 16 m/s. Assuming that the dart is uniformly accelerated, how long does it take for the dart to travel the length of the barrel?

Answer 1

For UNIFORM ACCELERATION, the relevant equation is

d = 1/2 (u + v) t,

where u (v) are the initial (final) speeds, d the length of the barrel, and t the time taken.

So t = 2d/v in this application.

Thus t = 3.4/16 s = 0.2125 s.

Live long and prosper.

Answer 2

Assuming that everything started with a speed of zero (before the blow started):

distance (1.7 m) = (0.5)*a*t^2
speed (16 m/s) = a*t

where t is the time (in seconds) from the start of the blow to the exit of the dart and a is the acceleration (in metres per second squared: m / s^2).

Two unknowns, two variables, go for it.

The easy way is by substitution. Find t relative to a, using the second equation. Then put that instead of t in the first one (don't forget to square everyting that you are putting in for t)