a) Find the average velocity of the dot between t=0 and t=2.0s. Give your answer

Question

a) 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.For example, if you think thexcomponent is 3 and theycomponent is 4, then you should enter3,4.

b) Find the instantaneous velocity at t=0. Give your answer as a pair of components separated by a comma.

c) Find the instantaneous velocity at t=1.0s. Give your answer as a pair of components separated by a comma.

d) Find the instantaneous velocity at t=2.0s. Give your answer as a pair of components separated by a comma.

Explanation / Answer

r= [ 4.2 cm + (2.30cm/s2)t2] i + (5.10cm/s)t j

velocity = dr/dt = (2.30 x 2t cm/s)i +( 5.10 cm/s) j = 9.2 i + 5.1 j

velocity at t=0,= 5.10 cm/s j

vecity at t=2,= (2.30 x 2 x 2) i + 5.10 j

(i) Average velocity = (vto +vt=2)/2

= [9.2 i +( 5.1 +5.1)j]/2

=(4.6 i + 5.1 j) (Ans)

(ii) instantaneous velocity at t=0,= (dr/dt)t=0 =5.10 cm/s j

= 0,5.10 (Ans)

(iii)instantaneous velocity at t=1.0,= (dr/dt)t=1 = (2.30 x 2 x 1cm/s) i +5.10 cm/s j

= 4.6 cm/s i + 5.1 cm/s j

= 4.6,5.1 (Ans)

(iv) instantaneous velocity at t=2.0,= (dr/dt)t=2 = (2.30 x 2 x 2cm/s) i +5.10 cm/s j

= 9.2 cm/s i + 5.1 cm/s j

= 9.2, 5.1 (Ans)

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