A web page designer creates an animation in which a dot on a computer screen has position ⃗r=[4 cm + (2.5cm/s 2) t 2 ] ^ i + (5cm/s) t ^ j.

a) Find the magnitude and direction of the dot's average velocity between t=0 and t=2 s.

b) Find the magnitude and direction of the instantaneous velocity at t=0, t=1 s, and t=2 s. and show the velocities calculated in pan (b).

a)

r = (4 + 2.5 t²) i + 5 t j

When t = 0

r₁ = 4 cm i

When t = 2s

r₂ = 14 i + 10 j

Displacement

= r₂ - r₁

=14 i + 10 j - 4i

= 10i + 10j

average velocity

= displacement / time

= (10i + 10j) / 2

= 5i + 5j

b)

r = (4 + 2.5 t²) i + 5 t j

dr / dt = 5 t i + 5 j

Instantaneous velocity at t = o

(dr / dt) ₀ = 5 j

Instantaneous velocity at t = 1s

(dr / dt) ₁ = 5i + 5j

Instantaneous velocity at t = 2s

(dr / dt) ₂ = 10i + 5 j