Question

The following equation shows the position of a particle in time t, x=at2i + btj where t is in second and x is in meter. A=2m/s2, b=1m/s.
Find

A, the average velocity of the particle in the time interval t₁=2sec and t₂=3sec

B, the velocity and acceleration at any time t.

C, the average acceleration in the time interval given in part (a)​

Answer 1

(a) The average velocity of the particle in the time interval t₁=2sec and t₂=3sec is 10 m/s.

(b) The velocity and acceleration at any time t is v =  (4ti + j) m/s and a = a = 4i m/s²

(c)  The average acceleration in the time interval given in part (a)​ is 3.98 m/s².

Position of the particle

x = at²i + btj

x = 2t²i + tj

Average velocity, at t₁=2sec and t₂=3sec

Δv = Δx/Δt

x(2) = 2(2)²i + 2j

x(2) = 8i + 2j

|x(2)| = √(8² + 2²) = 8.246

x(3) =  2(3)²i + 3j

x(3) = 18i + 3j

|x(3)| = √(18² + 3²) = 18.248

Δv = (18.248 - 8.246)/(3 - 2)

Δv =  10 m/s

Velocity and acceleration at any time, t

v = dx/dt

v =  (4ti + j) m/s

a = dv/dt

a = 4i m/s²

Average acceleration

v(2) = 4(2)i + j

v(2) = 8i + j

|v(2)| = 8.06 m/s

v(3) = 4(3)i + j

v(3) = 12i + j

|v(3)| = 12.04 m/s

a = (12.04 - 8.06)/(3 - 2)

a = 3.98 m/s²

Learn more about average acceleration here: brainly.com/question/104491

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