Aweb 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).

Explanation:

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

-4 on