Question

). A particle is moving in a straight line such that its
velocity is given by v = 6 + 3t2. If at time
t = 0, the particle is at origin, then average velocity
during t = 0 to t = 2 s is (where v is in m/s and t is in s)
(1) 8 m/s
(2) 10 m/s
(3) -7 m/s
(4) – 10 m/s​

Answer 1

Answer:

Option (3)

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Answer 2

Dear Student,

◆ Answer -

(2) 10 m/s

● Explanation -

Given that -

v = 3t² + 6

To calculate displacement,

s = ʃv.dt

s = ʃ(3t²+6).dt

s = ʃ3t².dt + ʃ6.dt

s = t³ + 6t

Position of the particle at t = 0 s,

s0 = t³ + 6t

s0 = 0³ + 6×0

s0 = 0 m

Position of the particle at t = 2 s,

s2 = 2³ + 6×2

s2 = 20 m

Total displacement is calculated as -

s = s2 - s0

s = 20 - 0

s = 20 m

Average velocity iz calculated by -

vavg = s / t

vavg = 20 / 2

vavg = 10 m/s

Therefore, average velocity of the particle in 1st 2 s is 10 m/s.

Hope this helps you...