Understanding the Concepts
* Acceleration: The rate at which an object's velocity changes.
* Distance: The total length traveled by an object.
The Missing Information
To calculate distance, we need to know the object's initial velocity (v₀). Here's why:
* Scenario 1: Object Starts from Rest (v₀ = 0)
If the object starts at rest, the distance traveled is directly related to the acceleration and time.
* Scenario 2: Object Has an Initial Velocity (v₀ ≠ 0)
If the object already has a velocity when the acceleration starts, that initial velocity impacts the final distance traveled.
The Formula
The formula to calculate distance (d) with constant acceleration is:
d = v₀t + (1/2)at²
Where:
* d = distance
* v₀ = initial velocity
* t = time
* a = acceleration
Solving the Problem
Let's assume the object starts from rest (v₀ = 0):
1. Given:
* a = 0.5 m/s²
* t = 20 s
* v₀ = 0 m/s
2. Plug the values into the formula:
d = (0 m/s)(20 s) + (1/2)(0.5 m/s²)(20 s)²
3. Calculate:
d = 0 + (0.25 m/s²)(400 s²)
d = 100 meters
Therefore, if the object starts from rest, it will travel 100 meters in 20 seconds with an acceleration of 0.5 meters per second squared.
To get a different answer, you'll need to provide the initial velocity of the object.
