The velocity function for a particle is v (t) = 2t - 5 ft/sec. Find the displacement for the particle from t = 0 to t = 4 sec. (Give answer with units)

Displacement, d = - 4ft

Step-by-step explanation:

Given,

The velocity function for a particle v (t) = 2t - 5 ft/sec.

To obtain the displacement for the particle from t = 0 to t = 4 sec

We integrate v (t) with respect to t

: Displacement, d = ∫₀⁴ (2t - 5) dt

= t² - 5t |₀⁴ = (4² - 5 (4)) - 0² - 5 (0)

=16 - 20 = - 4ft

Answer: The displacement is - 4 ft.

Step-by-step explanation:

The velocity is:

v (t) = 2t - 5ft/s

If we want to find the displacement between t = 0s and t = 4s, we need to find the difference between the position at t = 0s and at t = 4s

The equation for the position is obtained by integrating over time:

P (t) = (2t^2) / 2 - 5*t + c

where c is the initial position, then we have:

P (t) = t^2 - 5t

P (4) - P (0) = 4*4 - 5*4 - 0 = 16 - 20 = - 4

The total displacement is - 4 feet