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 initial ( $t = 0$ ) velocity of the particle
A) is 0 m/s.
B) is 2.3 m/s.
C) is 23 m/s.
D) cannot be determined.

Question

Quizplus · Accepted Answer

The velocity of the particle is given by the derivative of the position function with respect to time, $v(t) = dx/dt$. For $x(t) = 23t - 1.2t^3$, $v(t) = d(23t - 1.2t^3)/dt = 23 - 3.6t^2$. At $t = 0$, $v(0) = 23 - 3.6(0)^2 = 23$ m/s.

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 $x ( t ) = 23 t - 1.2 t ^ { 3 }$