A. The average velocity of the particle in the time interval t₁=2sec and t₂=3sec is 4 i m/s.
B. The velocity and acceleration at any time t is 4t i +1 j and 4i.
C. The average acceleration in the time interval given in part (a) is 4
What is acceleration?
Acceleration can be defined as the rate change of velocity with time.
acceleration a = (Δv) / (Δt)
Given the following equation shows the position of a particle in time t, x=at² i + bt j
where t is in second and x is in meter. a=2m/s², b=1m/s.
A. Velocity is time rate of change of displacement.
V = dx/dt
V = d/dt (2t² i + 1t j)
V = 4t i +1 j
Velocity in time interval,
At t₁=2sec , V₂= 4x2 i + 1 j = 8 i + 1 j
At t₂=3sec, V₃ = 4x3 i + 1 j = 12 i + 1 j
Average velocity in time interval t₁=2sec and t₂=3sec is
, V₃ - V₂ = (12 i + 1 j) - ( 8 i + 1 j )
Average velocity = 4 i
B. Velocity at time t, is
V(t) = V = 4t i +1 j
Acceleration a = dV/dt
a(t) = d/dt (4t i +1 j)
a(t) = 4 i +0 j
C. Average acceleration in time interval t₁=2sec and t₂=3sec is
a = 4 m/s²
Learn more about acceleration.
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