Final answer:
To find the time taken for an object with an acceleration of 34 m/s² to travel 3400 m, the kinematic equation s = ½at² is used. With the initial velocity being zero, the time (t) calculated is 14 seconds.
Step-by-step explanation:
We need to find the time it takes for an object starting from rest, with an acceleration of 34 m/s², to travel a distance of 3400 m. To solve this problem, we'll use the kinematic equation for uniformly accelerated motion, which relates distance (s), initial velocity (u), acceleration (a), and time (t):
s = ut + ½at²
Given that the initial velocity (u) is 0 m/s (as the object starts from rest), the equation simplifies to:
s = ½at²
Let's plug in our values:
3400 m = ½ × 34 m/s² × t²
By rearranging the equation and solving for t, we get:
t² = × (2 × 3400 m) / (34 m/s²)
t = √(6800 / 34)
t = 14 s
It will take the object 14 seconds to travel 3400 meters at an acceleration of 34 m/s².