Question

The force acting on a body moving in a straight line is
given by F = (3t2+– 4t+1) Newton where t is in sec. If
mass of the body is 1kg and initially it was at rest at
origin. Find displacement between time t= 0 and t = 2
sec. (use F=ma)​

Answer 1

$f = 3 {t}^{2} - 4t + 1$
We know Force = mass(acceleration)


and
$a = 3 {t }^{2} - 4t + 1$


As
$a = \frac{dv}{dt} \\ dv = a(dt)$

Integrating a will give velocity

as done in the 1st image above (add constant Z at the end please),

Since initial velocity was 0 the constant Z will be 0 there.

Integrating it again will give displacement, (2nd image)
once again the constant will be 0 since at t=0 the body was at rest.
substitute for 0 and 2 and subtract them,


0-( 4-21.3 +2)
= -(6-21.3)
= -(-15.3)
= 15.3

Therefore the displacement was 15.3 m.