The maximum speed at which the car can maintain the same
motion is 4.7 m/s
The total mass of the car = 1200 kg
The is climbing the slope which is at an angle of 18°
The maximum power its engine can provide = 18.2 kw
The maximum speed of the car can maintain in the same motion can be found using the formula,
P = F x v x cosθ
where P is the power
F is the force
v is the velocity
θ is the slope angle
The force of the car on the slope can be found using the formula
F = f x mgsinθ
where f is the frictional force
For attaining maximum speed at the same motion, frictional force will be zero
Therefore , F = 1200 x 9.8 x sin 18°
F = 11,760 x 0.309
= 3,634 N
Now let us substitute the known values in the power formula, we get
18.2 x 10³ = 3,634 x v x cos 18°
v = 18.2 x 10³ / 3,634 x cos 18°
= 18.2 x 10³ / 3,634 x 0.95
= 18.2 x 10³/ 3,825.26
= 0.0047 x 10³
v = 4.7 m/s
Therefore, the maximum speed of the car is 4.7 m/s
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