Calculating Stopping Distance for Truck A
We need to find the distance Truck A travels before stopping. We use the kinematic equation $v^2 = u^2 + 2as$, where:
- $v$ is the final velocity ($0 \ m/s$ as it stops)
- $u$ is the initial velocity ($16 \ m/s$)
- $a$ is the acceleration (deceleration, so $-2 \ m/s^2$)
- $s$ is the distance traveled
Plugging in the values:
$0^2 = (16 \ m/s)^2 + 2(-2 \ m/s^2)s_A$
$0 = 256 \ m^2/s^2 - (4 \ m/s^2)s_A$
$s_A = \frac{256 \ m^2/s^2}{4 \ m/s^2} = 64 \ m$
Truck A travels $64 \ m$ before stopping.
Calculating Stopping Distance for Truck B
Similarly, we find the distance Truck B travels before stopping using the same kinematic equation $v^2 = u^2 + 2as$. For Truck B:
- $v = 0 \ m/s$
- $u = 20 \ m/s$
- $a = -4 \ m/s^2$
Substituting the values:
$0^2 = (20 \ m/s)^2 + 2(-4 \ m/s^2)s_B$
$0 = 400 \ m^2/s^2 - (8 \ m/s^2)s_B$
$s_B = \frac{400 \ m^2/s^2}{8 \ m/s^2} = 50 \ m$
Truck B travels $50 \ m$ before stopping.
Determining Final Distance Between Trucks
The initial distance between the trucks was $200 \ m$. When they stop, the total distance covered by both trucks is the sum of their stopping distances.
Total distance covered $= s_A + s_B = 64 \ m + 50 \ m = 114 \ m$.
The final distance between them is the initial distance minus the total distance they covered while braking.
Final distance $= \text{Initial Distance} - (s_A + s_B)$
Final distance $= 200 \ m - 114 \ m = 86 \ m$.
Therefore, the distance between the trucks when they stop is $86 \ m$.
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