Find Displacement (s)

Classical Mechanics Level 2

If Equation for acceleration(a) = 3t + 2 , At t = 0 velocity = 4m/s .

Find the displacement at t = 6 seconds ( in meters ) .If displacement at t = 2 seconds is 32m .


The answer is 184.

Lakshya Khilwani by Lakshya Khilwani , 17, India

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1 solution

Aryan Sanghi
Oct 19, 2018

a=3t+2

v= ∫ a d t \int adt

v= 3 t ² 2 \frac{3t²}{2} +2t+C

Putting t=0 and v=4, we get C=4

v= 3 t ² 2 \frac{3t²}{2} +2t+4

s= ∫ v d t \int vdt

s= t ³ 2 \frac{t³}{2} +t²+4t+D

Putting t=2 and s=32, we get D=16

s= t ³ 2 \frac{t³}{2} +t²+4t+16

Putting t=6 we get s=184

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