The position of a particle which moves along a straight line is defined by: x=t^3-6t^2-15t+40, where x is in feet and t is in seconds. Determine the time at which the velocity will be zero, the position and distance traveled at that time, and the acceleration of the particle at that time.
Velocity is defined as dx/dt (rate of change of displacement).
thus V = dx/dt = 3 t^2 - 6*2 t - 15.
When V=0,we get a quadratic equation 3 t^2 - 6*2 t - 15 = 0 ...
The solution addresses the position of a particle. The time, position, distance, and acceleration all have to be determined with respect to this particle moving along a straight line.