Question

The motion of a particle is defined by the relation S=2t3-15t2+24t+4 where S is expressed in metres and t in seconds. Determine when the velocity is zero

Answer 1

Answer on Question #66185, Physics | Mechanics | Relativity

Question

The motion of a particle is defined by the relation $S = 2t^3 - 15t^2 + 24t + 4$ where $S$ is expressed in metres and $t$ in seconds. Determine when the velocity is zero.

Solution

Velocity is the first derivative of the path at the time. Find the equation of speed

$$V = S' = 6t^2 - 30t + 24$$

Determine the time when velocity is zero, it will set up and solve the equation

$$V = 0$$ $$6t^2 - 30t + 24 = 0$$ $$t^2 - 5t + 6 = 0$$

Theorem the inverse vieta theorem we get

$$t_1 = 2s$$ $$t_2 = 3s$$

Answer $t_1 = 2s, t_2 = 3s$.

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