The position of a particular particle as a function of time is given by r⃗ = ( 9.60t⋅i^ + 8.85j^ – 1.00t2⋅k^)m, where t is in seconds.
Express your answer in terms of the unit vectors i^,j^, and k^.
2 Answers

When t=1.00s, the position is
r⃗ ₁ = ( 9.60(1.00)î + 8.85ĵ – 1.00(1.00)²k̂ ) m
. . = ( 9.60î + 8.85ĵ – 1.00k̂ ) m
When t=3.00s, the position is
r⃗ ₂ = ( 9.60(3.00)î + 8.85ĵ – 1.00(3.00)²k̂ ) m
. . = ( 28.8î + 8.85ĵ – 9.00k̂ ) m
Displacement Δr⃗ is r⃗ ₂ – r⃗ ₁ and time interval is Δt = (3.00 – 1.00)s = 2.00s
Average veocity v⃗ = Δr⃗ /Δt
= [ ( (28.89.60)î + (8.858.85)ĵ – (9.00(1.00)k̂ ) ] / 2.00 m/s
= [ ( 19.2î + 0ĵ – 8.00k̂ ) ]/2.00 m/s
= ( 9.6î + 0ĵ – 4.00k̂ ) m/s

r⃗ = ( 9.60t⋅i^ + 8.85j^ – 1.00t2⋅k^)m,
So,
For, t= 1sec, r(1) = ( 9.60⋅i^ + 8.85j^ – 1.00t2⋅k^)m, ………………………… [1]
and
For, t = 3 sec, r(3) = ( 9.60*3⋅i^ + 8.85j^ – 1.00t2⋅k^)m = ( 28.80⋅i^ + 8.85j^ – 1.00t2⋅k^)m, ……. [2]
So,
Average velocity = [r(3) – r(10] / (3 – 1) =( 14.40⋅i^ + 0.0j^ – 0.02⋅k^)m/sec. <——————/