To calculate the speed of the car at the bottom of the driveway, we can use the principle of conservation of energy.
The initial potential energy (PE) of the car at the top of the driveway is given by:
PE = mgh
where m is the mass of the car (2.06×10³ kg), g is the acceleration due to gravity (9.8 m/s²), and h is the height of the driveway (4.35 m).
PE = (2.06×10³ kg)(9.8 m/s²)(4.35 m)
= 8.96×10⁴ J
The work done by the friction force is given by:
Work = Force x Distance
The friction force is given as 3.93×10³ N, and the distance is 4.35 m.
Work = (3.93×10³ N)(4.35 m)
= 1.71×10⁴ J
The final kinetic energy (KE) of the car at the bottom of the driveway is equal to the initial potential energy minus the work done by friction:
KE = PE - Work
= 8.96×10⁴ J - 1.71×10⁴ J
= 7.25×10⁴ J
The kinetic energy is given by:
KE = 1/2 mv²
where v is the velocity of the car at the bottom of the driveway.
Rearranging the equation, we have:
v² = 2KE / m
v² = (2)(7.25×10⁴ J) / (2.06×10³ kg)
v² = 7.05×10⁴ J / (2.06×10³ kg)
v² = 34.22 m²/s²
Taking the square root of both sides, we get:
v = √(34.22 m²/s²)
v ≈ 5.85 m/s
Therefore, the speed of the car at the bottom of the driveway is approximately 5.85 m/s.