Question

speed of a particle moving in a straightline varies with time as v=(3+2t)m/s.the distance covered in first 3 seconds is​

Answer 1

Answer :

• Distance covered in 3s is 18 m

Explanation :

• v = (3 + 2t)

$\longrightarrow \sf{v \: = \: (3 \: + \: 2t)} \\ \\ \longrightarrow \sf{\dfrac{dx}{dt} \: = \: (3 \: + \: 2t)} \\ \\ \longrightarrow \sf{dx \: = \: (3 \: + \: 2t)dt} \\ \\ \longrightarrow \sf{\int dx \: = \: \int (3 \: + \: 2t)dt} \\ \\ \longrightarrow \sf{x \: = \: 3t \: + \: t^2} \\ \\ \underline{\underline{\sf{Displacement \: is \: 3t \: + \: t^2 \: m}}}$

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Put t = 3

$\longrightarrow \sf{x \: = \: 3(3) \: + \: (3)^2} \\ \\ \longrightarrow \sf{x \: = \: 9 \: + \: 9} \\ \\ \longrightarrow \sf{x \: = \: 18} \\ \\ \underline{\underline{\sf{Distance \: covered \: in \: 3 \: s \: is \: 18 \: m}}}$

Answer 2

Answer:

in 3 second 27meter covered