The displacement of particle moving along on x axis is given by x = 18t + 5.0t^2, where x is in meters and t is in seconds Calculate : the instantaneous velocity at t = 2.0 s the average velocity between t = 2.0 and t = 3.0 s

38 m/s

43 m/s

Explanation:

x = 18t + 5.0t²

The instantaneous velocity is the first derivative:

v = 18 + 10. t

At t = 2.0:

v = 18 + 10. (2.0)

v = 38 m/s

The average velocity is the change in position over change in time.

v = Δx / Δt

v = [ (18t₂ + 5.0t₂²) - (18t₁ + 5.0t₁²) ] / (t₂ - t₁)

Between t = 2.0 and t = 3.0:

v = [ (18 (3.0) + 5.0 (3.0) ²) - (18 (2.0) + 5.0 (2.0) ²) ] / (3.0 - 2.0)

v = [ (54 + 45) - (36 + 20.) ] / 1.0

v = 99 - 56

v = 43 m/s