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Answer :
Final answer:
To find the speed of the car at the bottom of the driveway, we can use the parallel force of gravity and subtract the friction force to find the net force. Using Newton's second law and the kinematic equation, we can find the acceleration and final velocity of the car respectively.
Explanation:
To find the speed of the car at the bottom of the driveway, we can break the weight of the car into components parallel and perpendicular to the inclined plane. The force parallel to the incline is equal to the force of gravity times the sine of the angle of inclination. Subtracting the friction force from this parallel force gives us the net force. Using Newton's second law, we can find the acceleration of the car. Finally, using the kinematic equation for motion with constant acceleration, we can find the final velocity of the car.
Using the given values:
- The weight of the car (mg) = (2.1 x 10^3 kg) x (9.8 m/s²) = 2.058 x 10^4 N
- The force parallel to the incline = (2.058 x 10^4 N) x sin(16°) = 5.553 x 10^3 N
- The net force = (5.553 x 10^3 N) - (4.0 x 10^3 N) = 1.553 x 10^3 N
Using Newton's second law (F = ma) with the net force, we can find the acceleration:
1.553 x 10^3 N = (2.1 x 10^3 kg) x a
a = 1.553 x 10^3 N / (2.1 x 10^3 kg) = 0.739 m/s²
Finally, using the kinematic equation:
v^2 = u^2 + 2as
Where v is the final velocity, u is the initial velocity (0 m/s), a is the acceleration, and s is the displacement (4.2 m).
v^2 = (0 m/s)^2 + 2(0.739 m/s²)(4.2 m) = 6.2028 m²/s²
v = √(6.2028 m²/s²) ≈ 2.49 m/s
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