Final answer:
To solve for displacement or time in physics, we use kinematic equations, substituting known values into equations like x = xo + vt and v = vo + at to find the unknowns.
Step-by-step explanation:
Solving for Displacement in Physics
To solve for final displacement (xf), we can use the kinematic equation x = xo + vt. In this scenario, we are given that the initial velocity (vo) is 4.00 m/s, the time interval (Δt) is 2.00 minutes which needs converting to seconds, and the initial position (xo) is 0 m. First, we convert the time from minutes to seconds (2 minutes × 60 seconds/minute = 120 seconds). Then we substitute the known values into the equation: xf = 0 m + (4.00 m/s × 120 s), resulting in a calculation for xf.
Solving for Time 't'
The equation v = vo + at can be used to solve for time ('t') if the acceleration ('a') and the final and initial velocities (v and vo) are known. By rearranging the equation to solve for 't', we get t = (v - vo)/a. We identify the knowns from the question, substitute them into the equation, and solve for 't'.
Considering Initial Conditions and Acceleration
When an object starts from rest, its initial velocity (vo) is 0, and if the initial position (xo) is also 0, the equation simplifies to x = 1/2 at² when solving for displacement. The known acceleration and time are substituted to find x.
For a stationary object, calculating the gradient of the velocity vs. time graph will give us zero because the change in position over the change in time is zero, indicating no movement.
When given a velocity function (v(t)), the speed at different times can be acquired by evaluating the function at those times. The speed is the absolute value of the velocity, indicated by the modulus of v(t).
Summary
The provided equations are fundamental kinematic equations used in physics to determine various quantities such as displacement, time, and velocity based on known initial conditions and given parameters. Carefully selecting the right formula and rearranging it to solve for the unknown is essential in physics problems.