Final answer:
To calculate instantaneous velocity without calculus, one can simply substitute the specific time into the velocity equation or visually determine the value from a velocity vs. time graph. To find speed, take the absolute value of the instantaneous velocity.
Step-by-step explanation:
To calculate instantaneous velocity, one typically uses principles of calculus, specifically the concept of a derivative, which provides a precise rate of change at a given instant in time. However, an understanding of calculus is not always necessary for finding instantaneous velocity in certain simplifications or specific examples.
Instantaneous velocity is the velocity of an object at a specific moment in time. It's different from average velocity, which is the total displacement divided by the total time taken. For calculating instantaneous velocity in a practical scenario without calculus, one can visually determine the value from a velocity vs. time graph. At any given point on the graph, the instantaneous velocity is the value of the function at that point in time, which could also be the slope of the tangent line at that point on a position vs. time graph.
In an example with a jet car, to find the instantaneous velocity at t = 5 s, we could use the provided equation for v(t), where the instantaneous velocity might be given directly or through a calculation involving the rate of change or difference in position over a very tiny time interval approaching zero. If the velocity is constant, as in the example, the instantaneous velocity at t = 5 s is simply the velocity value at that time, which might be 40 m/s.
Speed is the magnitude of the velocity vector and doesn't include the directional component. To calculate speed from the instantaneous velocity, one would simply take the absolute value of the velocity vector, essentially ignoring the direction.
For instance, if the instantaneous velocity is -31 m/s, the speed is 31 m/s. If the value is positive, as in 40 m/s, the speed remains 40 m/s.