Question

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)

Answer 1

Displacement, d = - 4ft

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 2

Answer: The displacement is -4 ft.

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