Final answer:
To calculate the final velocity using time and displacement, we can use kinematic equations, or analyze the area under a velocity vs. time graph to calculate displacement, and then use average velocity formulae to derive the final velocity.
Step-by-step explanation:
To find the final velocity using time and displacement, one can employ kinematic equations or analyze motion graphs. To calculate displacement, the area under a velocity vs. time graph can be used, which gives the displacement as it represents the integral of velocity with respect to time. If you have the initial velocity, and you know the object is moving with constant acceleration, you can also use the second kinematic equation, which states that the average velocity is equal to the initial velocity plus the final velocity divided by two. This average velocity can then be multiplied by time to find displacement. If acceleration is known, another option is to find the final velocity through the rearranged definition of acceleration (final velocity = initial velocity + acceleration × time).
For instance, if a graph of velocity versus time is provided, we could derive the displacement. If we consider the first half of a trip with a constant velocity as shown in a graph similar to Figure 2.16, the displacement is the product of velocity and time. Therefore, using the formula d = v × t, where d is displacement, v is velocity, and t is time, we would calculate the displacement as the area under the velocity vs. time graph. Once we have the displacement and the time, we can use the formula for average velocity (displacement divided by time) to find the final velocity.