Question
5. You are driving a 3500 kg truck home from school one day when you notice a tree on the highway ahead. You slam on your brakes to avoid hitting the tree.Your brakes exert an average force of 2.0times 10^4 N of force leaving a skid mark that is 54.69 m long Use this information to calculate the initial speed of the truck in m/s & km/h
Solution
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Samuel
Master · Tutor for 5 years
Answer
Here's how to calculate the initial speed of the truck:**1. Understand the Physics**The work done by the brakes is equal to the change in the truck's kinetic energy. Since the truck comes to a stop, the final kinetic energy is zero.* Work = Force x Distance* Change in Kinetic Energy = Final Kinetic Energy - Initial Kinetic Energy = 0 - (1/2)mv²Therefore: Force x Distance = -(1/2)mv²**2. Solve for Initial Velocity (v)*** Force (F) = 2.0 x 10⁴ N* Distance (d) = 54.69 m* Mass (m) = 3500 kgRearranging the equation: v² = -2(F*d)/mSubstituting the values: v² = -2 * (2.0 x 10⁴ N * 54.69 m) / 3500 kgv² = 624.97 m²/s²v = √624.97 m²/s² v ≈ 25 m/s**3. Convert to km/h*** 1 m/s = 3.6 km/hTherefore: v ≈ 25 m/s * 3.6 km/h/m/s ≈ 90 km/h**Answer:**The initial speed of the truck was approximately 25 m/s or 90 km/h.