V(t)=t^2+2 (m/s) for t=0, x(0)=4m find the acceleration and the kinematic equation

Acceleration can be found by differentiating v(t) by t:

dv/dt =d(t^2+2)/dt

=d(t^2)/dt + d(2)/dt

=2tdt/dt + 0

=2t

The displacement x(t) can be found by integrating v(t) by t

x(t) = int(t^2 + 2)dt

= t^3/3 + 2t + c

When t=0, x(0)=4=0+0+c

So c=4

x(t) = t^3/3 + 2t + 4

v(t) = t^2 + 2

a(t) = 2t

cant without the picture! ?

when jerome paddle in flowing river towards east the net speed of jerome will increase

so the net speed of jerome will be given as

now the speed of paul will be same as it is given as he is running on the ground

so

so here we can say since the speed of jerome is more so he will win the race

now as we know the distance so the time difference is given as

so jerome will reach first and the time difference will be 203.55 s or 3.4 min