Question

A particle moves along the x-axis (units in cm). Its initial position at t=0 sec is f(0) = 13. The figure shows the graph of the particle's velocity f'(t). Thenumbers are the areas of the enclosed regions.

The position of other particle at t = c, is given by f(c). What is the position of the particle at time t = c?

Answer 1

Answer:

  f(c) = -54 cm

Step-by-step explanation:

You want the position of a particle at t=c, given f(0) = 13 cm and the velocity f'(t) graph is shown.

Area

The area under the velocity curve has units of (cm/s)×(s) = cm. When the area is below the time axis, the change in position is negative.

The position at t = c will be the sum of the initial position and the changes indicated by the velocity curve.

  (position at t=c) = (13 cm) -(11 cm) +(14 cm) -(70 cm) = -54 cm

The position of the particle at t = c is f(c) = -54 cm.