The driver of a truck slams on the brakes when he sees a tree blocking the road. The truck slows down uniformly with acceleration −5.80 m/s2 for 4.20 s, making skid marks 57.2 m long that end at the tree. With what speed does the truck then strike the tree?
Vi=Vf-at
Vi=2xt-Vf
Vf-at=2xt-Vf
Vf-(-5.8 x 4.20) = 2(57.2 x 4.2)-Vf
Solve for final velocity = 228.06 but that answer is incorrect.
Well, it seems like you're trying to solve a physics problem. But don't worry, I'm here to lighten the mood! Instead of thinking about the truck crashing into a tree, let's imagine it crashing into a giant pillow fort. That sounds much more enjoyable, don't you think?
Now, back to the problem. To find the final velocity of the truck, we can use the equation:
Vf = Vi + at
The initial velocity (Vi) is not given, but we know that it is zero since the truck is coming to a stop. So, we can simplify the equation to:
Vf = at
Plugging in the values, we get:
Vf = -5.8 m/s^2 x 4.2 s
Now, all we need to do is calculate:
Vf = -24.36 m/s
So, the truck speeds into the tree at a cozy -24.36 m/s. Remember, this is just a theoretical pillow fort crash, so no actual trees were harmed in the making of this answer!
Let's calculate the final velocity correctly.
We have the initial velocity (Vi) as 0 m/s because the truck was at rest before braking.
We can use the equation of motion, which relates the final velocity (Vf), initial velocity (Vi), acceleration (a), and time (t):
Vf = Vi + at
Plugging in the given values:
Vf = 0 + (-5.8 m/s^2)(4.20 s)
Vf = -24.36 m/s
Since velocity cannot be negative, we can consider the magnitude of the velocity as the speed:
Speed = |Vf| = |-24.36 m/s| = 24.36 m/s
Therefore, the truck strikes the tree with a speed of 24.36 m/s.
To solve this problem, we can use the kinematic equation that relates initial velocity (Vi), final velocity (Vf), acceleration (a), and displacement (d):
Vf^2 = Vi^2 + 2ad
In this case, the initial velocity (Vi) is 0 m/s because the truck initially comes to a stop. The acceleration (a) is -5.80 m/s^2 because the truck is slowing down. The displacement (d) is given as 57.2 m, which is the length of the skid marks.
Plugging in these values, we have:
Vf^2 = 0^2 + 2(-5.80)(57.2)
Vf^2 = 0 + (-66.96)(57.2)
Vf^2 = -3831.552
Taking the square root of both sides to solve for Vf, we get:
Vf ≈ ±√(-3831.552)
This leads to a problem because the result is imaginary, meaning that there is no real solution for the final velocity. In other words, the truck does not strike the tree.
It's worth noting that this result may seem counterintuitive since if the truck is slowing down, it should eventually come to a complete stop and collide with the tree. However, in this scenario, the given acceleration (-5.80 m/s^2) is not enough to bring the truck to a stop within the given time (4.20 s) and distance (57.2 m).
Therefore, there may be some data missing or erroneous in the problem statement. It's a good idea to double-check the problem or consult with the instructor if you are working on an assignment.