Car A and car B start moving simultaneously in the same direction along the line joining them. Car A with a constant acceleration a=4 m/s2, while car B moves with a constant velocity v=1 m/s. At time t=0, car A is 10 m behind car B. Find the time when car A overtakes car B.
Given uA=0,uB=1m/s,aA=4m/s2andaB=0
Assuming car B to be at rest, we have
uAB=uA−uB=0−1=−1m/s
aAB=aA−aB=4−0=4m/s2
Now, the problem can be assumed in simplified form as follows:
Substituting the proper values in equation
s=ut+12at2
we get 10=−t+12(4)(t2)
or 2t2−t−10=0
or t=1±√1+804=1±√814
1±94ort=2.5sand−2s
Ignoring the negative value, the desired time is 2.5 s.