The Mini Cooper is rated at a maximum power of 115. hp (1 hp=746 W), when moving at 80.0 km/h.
Assume that the net force accelerating the car is constant.
The total mass of the car with a rider and some fuel is 1230 kg.
How many seconds will it take for this car to go from zero to 100. km/h?
To find the time it takes for the car to accelerate from zero to 100 km/h, we need to determine the acceleration first.
Given:
- Maximum power of the Mini Cooper = 115 hp
- Maximum power in watts = 115 hp * 746 W/hp
- Maximum power in watts = 85790 W
- Speed at which power is given = 80.0 km/h
Now, power is defined as the rate at which work is done or the rate at which energy is transferred. In this case, the power output of the car's engine is 85790 W. Let's assume this power output is used only to overcome the air resistance and the force of friction. Therefore, we can say that power = force * velocity.
Force = power / velocity
Force = 85790 W / 80.0 km/h
Before proceeding, we need to convert the velocity from km/h to m/s.
Velocity = 80.0 km/h * (1000 m/km) / (3600 s/h)
Plugging in the values:
Force = 85790 W / (80.0 km/h * (1000 m/km) / (3600 s/h))
Force = 11.946 N (approximately)
Now, using Newton's second law of motion, we know that force equals mass times acceleration (F = m * a). Rearranging the equation, we get:
Acceleration (a) = Force (F) / Mass (m)
Acceleration (a) = 11.946 N / 1230 kg
Acceleration (a) = 0.0097 m/s² (approximately)
Now we can use the kinematic equation to find the time it takes to accelerate from zero to 100 km/h:
v = u + at
Where:
v = final velocity (100 km/h)
u = initial velocity (0 m/s)
a = acceleration (0.0097 m/s²)
t = time
Rearranging the equation, we get:
t = (v - u) / a
Substituting the values:
t = (100 km/h * (1000 m/km) / (3600 s/h) - 0 m/s) / 0.0097 m/s²
Calculating the value:
t = 11.42 s (approximately)
Therefore, it will take approximately 11.42 seconds for the car to accelerate from zero to 100 km/h.