Question

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

Answer 1

38 m/s

43 m/s

Step-by-step 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