Question

A web page designer creates an animation in which a dot on a computer screen has a position of r =[ 4. cm +( 2 cm/s2 )t2]i^+( 5cm/s )tj^ .find the average velocity of the dot between t=0 and t=2.0s. give your answer as a pair of components separated by a comma.

Answer 1

The average velocity of the dot is calculated as the change in position over the time interval, which is 10 cm/s in the i direction and 5 cm/s in the j direction.

Step-by-step explanation:

The student has asked to find the average velocity of a dot between t=0 and t=2.0s given the position vector ℝ(t) = [4 cm + (2 cm/s2)t2]i^ + (5 cm/s)tj^. To find the average velocity, we need to calculate the change in position divided by the change in time. The position at t=0 is ℝ(0) = 4i^ + 0j^ and the position at t=2.0s is ℝ(2) = [4 + (2)(2)2]i^ + (5)(2)j^ = 4i^ + 20i^ + 10j^ = 24i^ + 10j^.

To find the average velocity, ρavg, we use the formula:

ρavg = [ℝ(2) - ℝ(0)] / Δt

Substitute the known values:

ρavg = [(24i^ + 10j^) - (4i^ + 0j^)] / (2.0s - 0s)

ρavg = (20i^ + 10j^) / 2.0s

ρavg = 10i^ + 5j^ cm/s

Therefore, the average velocity of the dot is 10 cm/s in the i direction and 5 cm/s in the j direction.