The driver of a truck slams on the brakes when he sees a tree blocking the road. The truck slows down uniformly with an acceleration of -5.60 m/s2 for 4.20 s, making skid marks 62.4 m long that end at the tree. With what speed does the truck then strike the tree?

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26.62

To find the speed at which the truck strikes the tree, we can use the kinematic equation:

v^2 = u^2 + 2as

Where:
v = final velocity (unknown)
u = initial velocity (assuming the truck was initially traveling at a constant speed, which we do not know)
a = acceleration (-5.60 m/s^2)
s = distance (62.4 m)

Since the truck slows down uniformly, the initial velocity (u) can be assumed to be the same as the final velocity right before it hit the tree.

Using the equation, we can rewrite it as:

v^2 = u^2 + 2as

v^2 = 0^2 + 2(-5.60 m/s^2)(62.4 m)

v^2 = 2(-5.60 m/s^2)(62.4 m)

v^2 = -696.96 m^2/s^2

Taking the square root of both sides, we get:

v = √(-696.96 m^2/s^2)

Using a negative square root may seem odd, but it's because the velocity is directed opposite to the positive direction (since it's slowing down).

Therefore, the speed at which the truck strikes the tree is approximately:

v ≈ -26.4 m/s

Note: The negative sign indicates that the truck is moving in the opposite direction (slowing down) compared to the positive direction.

To find the speed of the truck when it strikes the tree, we can use the equations of motion.

1. We know that the truck slows down uniformly, so the equation we can use is:
v = u + at
where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time period.

2. We're given the following information:
a = -5.60 m/s^2 (negative because it's deceleration)
t = 4.20 s
u = ?

3. Rearrange the equation to solve for u:
u = v - at

4. The initial velocity, u, is the speed of the truck before it started braking.

5. We also know that the truck initially traveled at a certain speed, covered a distance of 62.4 m, and came to a stop at the tree. This means that at the start, the velocity, u, was the speed of the truck, and at the end, the velocity, v, is 0 m/s. Therefore, we can rewrite the equation:

0 = u - at

6. Substitute the given values:

0 = u - (-5.60 m/s^2) * 4.20 s

7. Simplify the equation:

0 = u + 23.52 m/s

8. Solve for u:

u = -23.52 m/s

Therefore, the truck's initial speed before braking was -23.52 m/s. The negative sign indicates that the truck was originally moving in the opposite direction to its final motion.