Suppose a body has an initial velocity ‘u’ and a uniform acceleration ‘a’ for time ‘t’ so that its final velocity becomes ‘v’. Derive the equation for distance ‘s’ travelled by the body in this time.
Answers
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−t0Δt=tf−t0, taking t0=0t0=0 means thatΔt=tfΔt=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, x0x0 is the initial position and v0v0 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, Δt=tΔt=t. It also simplifies the expression for x displacement, which is now Δx=x−x0Δx=x−x0. Also, it simplifies the expression for change in velocity, which is now Δv=v−v0Δv=v−v0. To summarize, using the simplified notation, with the initial time taken to be zero,
Δt=tΔx=x−x0Δv=v−v0,Δt=tΔx=x−x0Δv=v−v0,