A particle moves along a straight line with equation of motion s = f(t), where s is measured in meters and t in seconds. Find the velocity and the speed when t = 3.

Question

f(t) = 18 + 20/t-1

Answer 1

Distance (s) is defined as f(t). Velocity is nothing more than the rate of change of distance traveled with respect to time (a.k.a. derivative of positional function). Velocity has a direction where as speed is the magnitude or evaluated velocity at a particular time.

If s = f(t) = 18 + 20/(t - 1) m

ds/dt = velocity = 20 * (t-1)^-2 m/s

ds/dt evaluated at t=3 --> 20/(3-1)^-2 = 5 m/s