Question

A particle's trajectory is described by x=(1/2t^3-2t^2)m and y=(1/2t^2-2t)m where t is in s. What is the particles speed at t=0?

Answer 1

The particle's speed at t=0 is 0 m/s.

Step-by-step explanation:

To find the particle's speed at t = 0, we need to calculate the magnitude of its velocity at that time. The velocity is given by the derivatives of the position equations:

v = dx/dt and u = dy/dt.

Substituting t = 0 into the velocity equations:

v(0) = 3(0) + 1.5(0)² = 0 m/s

u(0) = 1.5(0) - 2(0) = 0 m/s

As both the x and y components of the velocity are 0, the particle's speed at t = 0 is also 0 m/s.