The average velocity is 4i m/sec
The average acceleration is 4i
What is a average velocity ?
Average velocity is defined as the change in position or displacement (∆x) divided by the time intervals (∆t) in which the displacement occurs. T
According to the question,
x=at²i + btj ( t is in second and x is in meter).
Average velocity = [tex]\frac{dx}{dt}[/tex]
[tex]\frac{dx}{dt} = 2at i + b j\\\\\frac{dx}{dt} = 2 * 2 * t i +1 j\\\\\frac{dx}{dt} = 4t i +j[/tex]
[tex]\frac{dx}{dt}[/tex] in the time interval of 2 to 3 sec is
at 2 sec,
[tex]\frac{dx}{dt} = 4 * 2 i +j = 8i +j[/tex]
at 3 sec ,
[tex]\frac{dx}{dt}[/tex] = 4 * 3 i + j = 12i+j
Therefore the average velocity is
[tex]\frac{(12i +j - 8i -j)}{(3-2)} = 4i[/tex]
The velocity at any given time is [tex]\frac{dx}{dt} = 4t i +j[/tex]
The acceleration at any given time is [tex]\frac{dx^2}{dt^2}[/tex]
[tex]\frac{dx^2}{dt^2} = 4 i[/tex]
The average acceleration in the time interval t₁=2sec and t₂=3sec
Average Acceleration = 4i
Learn more about average velocity here:
https://brainly.in/question/11504533
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