Question

if v = 3t^2-2t+5 find displacement covered in time inertial 0 to 20 second
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Answer 1

Answer:

apply simple integration for solving:-

$v = 3 {t}^{2} - 2t + 5 \\ \frac{dx}{dt } = 3 {t }^{2} - 2t + 5 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: dx = 3 {t}^{2}.dt - 2t.dt + 5.dt \\ \: \: \: dx = 3 \frac{ {t}^{3} }{3 } - 2 \frac{ {t}^{2} }{2} + 5t \\ dx = {t}^{3} - {t}^{2} + 5t \\ x - 0 = ( {20}^{3} - {0}^{3} ) - ( {20}^{2} - {0}^{2} ) + 5(20 - 0)$

$x = 4000 - 400 + 100 \\ x = 3700m$

hope it helps..

Good luck ♧♧