To solve this problem, we can use the equations of motion for uniformly accelerating objects. The key equations we will use are:
1) v = u + at
2) s = ut + 0.5at^2
Where:
- v is the final velocity
- u is the initial velocity
- a is the constant acceleration
- t is the time
- s is the distance
Let's start by calculating the time it takes for the automobile and the truck to meet.
For the automobile:
Initial velocity, u1 = 0 m/s (since it starts from rest)
Acceleration, a1 = 2.10 m/s^2
For the truck:
Velocity, v2 = 15.1 m/s
Acceleration, a2 = 0 m/s^2 (since the truck maintain a constant speed)
Using Equation 1 for both the automobile and the truck:
v1 = u1 + a1 * t
v2 = u2 + a2 * t
Since the automobile starts from rest:
v1 = a1 * t
We can solve for time, t:
t = v2 / a1
t = 15.1 m/s / 2.10 m/s^2
t = 7.19 s (rounded to two decimal places)
Now that we know the time it takes for the truck and the automobile to meet, we can calculate the distance the automobile traveled.
Using Equation 2 for the automobile:
s = u1 * t + 0.5 * a1 * t^2
s1 = 0 * 7.19 s + 0.5 * 2.10 m/s^2 * (7.19 s)^2
s1 = 0 + 0.5 * 2.10 m/s^2 * 51.72 s^2
s1 = 54.27 m (rounded to two decimal places)
Therefore, the automobile overtakes the truck by traveling 54.27 meters beyond its starting point.
To find the velocity (speed) of the automobile when it overtakes the truck, we can use Equation 1 for the automobile:
v1 = u1 + a1 * t
v1 = 0 m/s + 2.10 m/s^2 * 7.19 s
v1 = 15.12 m/s (rounded to two decimal places)
So, the velocity (speed) of the automobile when it overtakes the truck is 15.12 m/s.