Final answer:
The time it takes for an object to travel 1000 meters with an acceleration of 5.2 m/s² is approximately 19.611 seconds, calculated using the kinematic equation s = ½ at².
Step-by-step explanation:
To calculate the time it takes for an object that begins to move from rest and travels 1000m with an acceleration of 5.2m/s², we use the equation of motion:
s = ut + ½ at²
where s is the displacement, u is the initial velocity, a is the acceleration, and t is the time.
Since the object starts from rest, u = 0, so the equation simplifies to:
s = ½ at²
Now we can insert the given values:
1000m = ½ × 5.2m/s² × t²
To find the time t, we rearrange the equation and solve for t:
t² = × 1000m / (0.5 × 5.2m/s²)
t² = 384.61538 s²
t = √ 384.61538 s²
t ≈ 19.611 s
So, it takes approximately 19.611 seconds for the object to travel 1000 meters with an acceleration of 5.2m/s².