VA= integer copy a(t)dt= integer 6dt =

3t

^2+2

2.

The displacement of a is

SA= integral vA(t)dt= integral (3t 2+2) dt = t 3+

2t

The displacement of b is

SB= integral vB(t)dt= integral (10t+ 1)dt=

5t

^2+t

When they met, they knew.

sA=sB+5

Alternative solution

t=5

now

sA=t^3+2t= 135

Plus the initial velocity, which is 3t 2+2. Only when integrating, the result of tdt integration is 1/2 * t 2, preceded by a coefficient 1/2. You can't use at to multiply directly, but adt to integrate.