A web page designer creates an animation in which a dot on a computer screen has

Question

A web page designer creates an animation in which a dot on a computer screen has a position of r = [ 4.3 cm +(2.6 cm/s^2)t^2]i + (4.8 cm/s)tj. Find the average velocity of the dot between t = 0 and t = 2.0 s. Give your answer as a pair of components separated by a comma. For example, if you think the x component is 3 and the y component is 4, then you should enter 3,4. Express your answer using two significant figures. Find the instantaneous velocity at t = 0. Give your answer as a pair of components separated by a comma. For example, if you think the x component is 3 and the y component is 4, then you should enter 3, 4. Express your answer using two significant figures. Find the instantaneous velocity at t = 1.0 s. Give your answer as a pair of components separated by a comma. For example, if you think the x component is 3 and the y component is 4, then you should enter 3,4. Express your answer using two significant figures. Find the instantaneous velocity at t 2.0 Give your answer as a pair of components separated by a comma. For example, if you think the x component is 3 and the y component is 4, then you should enter 3,4. Express your answer using two significant figures.

Explanation / Answer

part a)   The average velocity is displacement over time interval;
The position at t=0 and at t=2 is;

R(o) = 4.3(i)
R(2) = 14.7(i) + 9.6(j)

The average velocity is then;

v = [R(2) - R(0)]/(t-t0) = [10.4i +9.6j]/2 = 5.2i + 4.8j

The magnitude is

IvI = SqRt[vx^2 + vy^2] = SqRt[27.04 + 23.04] = 7.07 cm/s

part b)

To find instantaneous velocity differentiate position;

v = dR/dt = 5.2i + 4.8
The magnitude is;

v = SqRt[27.04t^2 + 23.04]
so at t=0

v=4.8

part c)

at t=1

v=7.07

part d)

at t=2

v=11.45

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.