A driver notices that her 1150-kg car slows down from 85 km/h to 65 km/h in about 6 seconds on the level when it is in neutral. Approximately what power (watts and hp) is needed to keep the car traveling at a constant 75 km/h?
As shown, a bead is sliding on a wire. How large must height h1 be if the bead , starting at rest at A, is to have a speed of 200 cm/s at point B? Ignore fiction
To find the power needed to keep the car traveling at a constant speed, we can use the equation:
Power = Force × Velocity
First, let's calculate the force required to slow down the car. We can use Newton's second law of motion, which states that the force acting on an object is equal to its mass multiplied by its acceleration:
Force = mass × acceleration
The acceleration can be calculated using the formula:
Acceleration = (final velocity - initial velocity) / time
Given:
Mass (m) of the car = 1150 kg
Initial velocity (v1) = 85 km/h
Final velocity (v2) = 65 km/h
Time (t) = 6 seconds
Converting the velocities from km/h to m/s:
v1 = 85 km/h × (1000 m/1 km) / (3600 s/1 h) ≈ 23.61 m/s
v2 = 65 km/h × (1000 m/1 km) / (3600 s/1 h) ≈ 18.06 m/s
Calculating the acceleration:
acceleration = (18.06 m/s - 23.61 m/s) / 6 s ≈ -0.93 m/s²
(Note: The negative sign indicates deceleration)
Now, we can calculate the force:
Force = 1150 kg × (-0.93 m/s²) ≈ -1070.5 N
(Note: The negative sign indicates opposite direction of motion)
Next, we need to calculate the power required to keep the car traveling at a constant speed of 75 km/h.
Converting the velocity from km/h to m/s:
Target velocity (v) = 75 km/h × (1000 m/1 km) / (3600 s/1 h) ≈ 20.83 m/s
Finally, we can calculate the power using the formula:
Power = Force × Velocity = -1070.5 N × 20.83 m/s
Power ≈ -22,334.9 watts
To convert the power to horsepower (hp), we can use the conversion factor:
1 horsepower (hp) ≈ 745.7 watts
Power in horsepower = -22,334.9 watts / 745.7 ≈ -29.95 hp
Approximately, the power needed to keep the car traveling at a constant 75 km/h is -22,334.9 watts or -29.95 horsepower. Note that the negative sign indicates that the engine or external force needs to produce power to overcome friction and maintain speed.