Summary
To find acceleration with time and displacement, we can use the formula a = (v_f - v_i) / Δt, where a is the acceleration, v_f is the final velocity, v_i is the initial velocity, and Δt is the change in time. This formula is derived from the definition of acceleration as the change in velocity per change in time. We can also use the formula d = v_i * t + 0.5 * a * t^2 to find displacement in terms of initial velocity, time elapsed, and constant acceleration.
Theorem
The theorem related to finding acceleration with time and displacement is the definition of acceleration as the change in velocity per change in time.
Physics Formula
The formula for finding acceleration with time and displacement is:
a = (v_f - v_i) / Δt
where:
– a is the acceleration
– v_f is the final velocity
– v_i is the initial velocity
– Δt is the change in time
We can also use the formula for displacement:
d = v_i * t + 0.5 * a * t^2
where:
– d is the displacement
– v_i is the initial velocity
– t is the time elapsed
– a is the acceleration
Physics Example
An example of finding acceleration with time and displacement is an object with an initial velocity of 0 m/s and a final velocity of 10 m/s after a time interval of 2 seconds. Using the formula a = (v_f - v_i) / Δt, we find that the acceleration is 5 m/s^2.
Physics Numerical Problem
A car travels 100 meters in 5 seconds with a constant acceleration. If the car’s initial velocity is 10 m/s, what is its final velocity?
To solve this problem, we can use the formula d = v_i * t + 0.5 * a * t^2 to find the acceleration:
a = (d - v_i * t) / (0.5 * t^2)
a = (100 m - 10 m/s * 5 s) / (0.5 * 5^2 s^2)
a = 12 m/s^2
Then, we can use the formula v_f = v_i + a * t to find the final velocity:
v_f = 10 m/s + 12 m/s^2 * 5 s
v_f = 70 m/s
Figure
A graph of velocity versus time for an object with constant acceleration would show a straight line with a constant slope.
Data Points
Data points that could be used to find acceleration with time and displacement include the initial and final velocities, the time interval, and the displacement.
Value
The value of acceleration can be measured in units such as m/s^2 or ft/s^2.
Measurements
Measurements that are needed to find acceleration with time and displacement include the initial and final velocities, the time interval, and the displacement.
Other Quantifiable Details
Other quantifiable details that could be relevant to finding acceleration with time and displacement include the mass of the object, the net force acting on the object, and the frictional forces acting on the object.
Technical Specification
A technical specification for finding acceleration with time and displacement would include the formula a = (v_f - v_i) / Δt, as well as the equations of motion for a uniformly accelerating object.
Theoretical Explanation
The theoretical explanation for finding acceleration with time and displacement is based on the definition of acceleration as the change in velocity per change in time, as well as the equations of motion for a uniformly accelerating object.
Reference Links
- Calculating the Acceleration of an Object from a Data Table – YouTube
- Lesson Explainer: Acceleration over Distance and Time | Nagwa
- How to Calculate Acceleration – Dummies.com
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