Question

a) The velocity of a moving body is t2 - t metres per second after a time of t seconds. Find the displacement of the body at the end of 12 seconds if the initial velocity is 0 metres per second.​

Answer 1

Explanation:

The integral of a velocity versus time function is a displacement versus time function

So we integrate,

${t}^{2} - t$

The integral of that is

$\frac{1}{3} {t}^{3} - \frac{ {t}^{2} }{2}$

Plug in 12 for t,

$\frac{1}{3} (12 {}^{3} ) - \frac{12 {}^{2} }{2}$

$576 - 72 = 504$

So the displacement is 504 meters to the right.

Answer 2

vf = 12² - 12 = 132 m/s

a = vf' = 2t-1

at t =12 s,

a = 2(12)-1 = 23 m/s²

vf²=vi²+2ad (vi=initial velocity=0)

vf²=2ad

132² = 2 x 23 x d

d = 378.78 m