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Answer 1

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First, let us make some simplifications in notation. Taking the initial time to be zero, as if time is measured with a stopwatch, is a great simplification. Since elapsed time is Δt = tf−t0, taking t0 = 0 means that Δt = tf, the final time on the stopwatch. When initial time is taken to be zero, we use the subscript 0 to denote initial values of position and velocity. That is, x0 is the initial position and v0 is the initial velocity. We put no subscripts on the final values. That is, t is the final time, x is the final position, and v is the final velocity. This gives a simpler expression for elapsed time—now, Δt=t. It also simplifies the expression for displacement, which is now Δx = x−x0. Also, it simplifies the expression for change in velocity, which is now Δv = v−v0. To summarize, using the simplified notation, with the initial time taken to be zero,