A particle of mass m =2kg starts from rest at the origin of an integral coordinate system at time t=0. A force F = 2 i + 4t j + 6t2 k is applied to it. Find the acceleration, velocity, and position of the particle for any latter time.
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Expert's answer
2021-01-12T12:10:33-0500
Given,
Mass of the particle (m) = 2kg
Particle starts from t = 0
Force F=2i^+4tj^+6t2k^
Acceleration of the particle a=mF
Hence, acceleration of the particle (a)=22i^+4tj^+6t2k^
⇒a=i^+2tj^+3t2k^
∣a∣=1+4t2+9t4
we know a=dtdv
Hence, dv=adt
Now, substituting the values, ∫dv=∫t=0t(i^+2tj^+3t2k^)dt
⇒∫dv=(ti^+212t2j^+313t3k^)
v=(ti^+t2j^+t3k^)
∣v∣=t2+t4+t6
We know that the relation between the position and the velocity is
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