The x and y positions (in meters)of a particle are given by: x(t)= 253 t,and y(t)= -12.0 t² + 155 t + 100.The speed of the particle at t = 12.9 s is A)0 m/s. B)98.4 m/s. C)296 m/s. D)408 m/s. E)529 m/s.

Question

Quizplus · Accepted Answer

The speed of the particle can be calculated using the following formula:

v(t) = sqrt[(dx/dt)^2 + (dy/dt)^2]

where dx/dt and dy/dt are the derivatives of x and y with respect to time, t.

Taking the derivatives of x and y, we get:

dx/dt = 253 m/s
dy/dt = -12.0 m/s

Substituting these values into the formula for speed, we get:

v(12.9) = sqrt[(253)^2 + (-12.0)^2] = 296 m/s

Therefore, the best choice is C, with an explanation that involves using the formula for speed and calculating the derivatives of x and y.

The X and Y Positions (In Meters)of a Particle Are