Car A accelerates from rest at 2m/s2. It passes Car B, which is at rest. Thirty (30) seconds later, the latter follows with a constant speed of 10m/s. Determine the distance in order to overtake the other.

Hi FEU students,

try to solve the distance of car A at 30 sec using s = v_o t + 1/2at^2

To determine the distance Car B needs to travel in order to overtake Car A, we need to consider the motion of both cars and find the point where they meet.

First, let's find the initial velocity of Car A. Since Car A accelerates from rest at 2 m/s^2 and has been accelerating for 30 seconds, we can use the formula v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time.

Given:
Acceleration of Car A (a) = 2 m/s^2
Time (t) = 30 s
Initial velocity of Car A (u) = 0 m/s (as it starts from rest)

Using the formula v = u + at, we can calculate the final velocity of Car A after 30 seconds:
v = u + at
v = 0 + (2 * 30)
v = 60 m/s

So, the final velocity of Car A after 30 seconds is 60 m/s.

Now, we need to find the time it takes for Car B to catch up to Car A. Since Car B travels with a constant speed of 10 m/s, we can set up an equation to find the time (t') it takes for Car B to travel the same distance as Car A.

Let d be the distance Car B needs to travel to overtake Car A.

For Car A:
Distance (s) = (1/2) * a * t^2
s = (1/2) * 2 * 30^2
s = 900 m

For Car B:
Distance (s') = v * t'
s' = 10 * t'
Since both cars meet at the same point, their distances are equal, so s' = s.

10 * t' = 900
t' = 900 / 10
t' = 90 s

Therefore, it takes Car B 90 seconds (t') to catch up to Car A.

Finally, to find the distance Car B needs to travel to overtake Car A, we can use the formula d = v * t', where d is the distance, v is the speed, and t' is the time.

d = 10 * 90
d = 900 m

So, Car B needs to travel a distance of 900 meters to overtake Car A.