Question

A particle moves in a straight line and it's velocity after t seconds is (t²- 3t - 2)m/s.

The distance of the particle from a fixed point on the line is Sm(S meters) after t seconds and S=10 when t=6. Find the formula for S in terms of t. ​

Answer 1

s = (1/3) t³ - (3/2) t² - 2t + 4

Explanation:

v = t² - 3t - 2

s = ∫v dt

= (1/3) t³ - (3/2) t² - 2t + c.

when s=10, t=6.

10 = (1/3) (6)³ - (3/2) (6)² - 2(6) + c

= 72 - 54 - 12 + c

= 6 + c

c = 10 - 6 = 4.

s = (1/3) t³ - (3/2) t² - 2t + 4