Question

The equation of motion of particle is s = 8t² + 3t - 10 ,s being in meters and t in seconds. Compute the initial velocity and also the velocity when the displacement is zero.

Answer 1

the velocity when the displacement is zero is 17.95 m/s.

Step-by-step explanation:

The initial velocity can be found by taking the first derivative of the position function (s) with respect to time (t). The velocity function v = ds/dt is given by:

v = 8 * 2t + 3

The initial velocity, v0, at t = 0, is:

v0 = 8 * 2 * 0 + 3 = 3 m/s

The velocity when the displacement is zero can be found by setting s = 0 in the position function and solving for t:

0 = 8t² + 3t - 10

Using the quadratic formula, we find that:

t = (-3 ± √(3² - 4 * 8 * -10)) / (2 * 8)

t = (-3 ± √(9 + 320)) / 16

t = (-3 ± √329) / 16

t = (-3 ± 18.12) / 16

t = (15.12 / 16) or (-21.12 / 16)

Since time cannot be negative, we take the positive value:

t = (15.12 / 16) = 0.9475 s

At t = 0.9475 s, the velocity can be found using the velocity function:

v = 8 * 2 * 0.9475 + 3 = 17.95 m/s

So, the velocity when the displacement is zero is 17.95 m/s.