Traveler a starts from rest at a constant acceleration of 6 m/s^2. two seconds later, traveler b starts with an initial velocity of 20 m/s at the same acceleration of 6 m/s^2. as measured by a, at what time will traveler b overtake traveler a?

a. 0.4s
b. 1.5s
c. 2.0s
d. 2.5s
e. 3.5s

3. 3.5 s

Explanation:

The position of traveller A is given by the equation:

where

is the acceleration of A

t is the time measured from when A started the motion

The position of traveller B instead is given by

where a (acceleration) is the same as traveller A, and

is B's initial velocity. We can verify that the formula is correct by substituting t=2, and we get , which means that B starts its motion 2 seconds later.

Traveller B overtakes traveller A when the two positions are the same, so: