a small 900kg sports car can deliver 100Hp to the pavement. how quickly can it reach 30m/s from rest?
change hp to watts.
1/2 m v^2=power*timeinseconds
solve for timeinseconds.
To calculate the time it takes for the small sports car to reach 30 m/s from rest, we need to use the basic physics equation:
v = u + at
where:
v = final velocity (30 m/s)
u = initial velocity (0 m/s, since the car is at rest)
a = acceleration (unknown)
t = time (unknown)
Now, we need to determine the acceleration of the car. In order to do that, we can use the following equation:
Power = Force x Velocity
Since the car is delivering 100 horsepower (Hp) to the pavement, we need to convert it to a more commonly used unit of power, which is watts (W). 1 horsepower is equal to 745.7 watts.
So, the power delivered by the car is:
Power = 100 Hp x 745.7 W/Hp = 74570 W
Now we need to consider the force acting on the car. The force can be determined using the equation:
Force = mass x acceleration
Since we know the mass of the car is 900 kg, we can rearrange the equation to find the acceleration:
acceleration = Force / mass
acceleration = 74570 W / 900 kg = 82.8 m/s^2 (rounded to one decimal place)
Now, we have the initial velocity, final velocity, and acceleration. We can rearrange the first equation to solve for time:
t = (v - u) / a
t = (30 m/s - 0 m/s) / 82.8 m/s^2 = 0.36 s (rounded to two decimal places)
Therefore, the small sports car will take approximately 0.36 seconds to reach a velocity of 30 m/s from rest.