The position of a particle is given by $x ( t ) = 23 t - 1.2 t ^ { 3 }$ , where x(t) is in meters and t is in seconds. The times ( $t \geq 0$ ) where the particle is located at the origin are
A) 0 seconds, 1.2 seconds.
B) 1.2 seconds, 23 seconds.
C) 0 seconds, 4.4 seconds.
D) 4.4 seconds, 23 seconds.

Question

Quizplus · Accepted Answer

To find when the particle is at the origin, set $x(t) = 0$: $23t - 1.2t^3 = 0$. Factoring gives $t(23 - 1.2t^2) = 0$, so $t = 0$ or $23 = 1.2t^2$. Solving $1.2t^2 = 23$ gives $t \approx 4.4$. Thus, the particle is at the origin at $t = 0$ and $t \approx 4.4$ seconds.

The Position of a Particle Is Given By x(t)=23t−1.2t3x ( t ) = 23 t - 1.2 t ^ { 3 }x(t)=23t−1.2t3

The Position of a Particle Is Given By $x ( t ) = 23 t - 1.2 t ^ { 3 }$