How long will it take an 850 kg car with 40 hp (horsepower) to reach the speed of 15 m/2, neglecting friction?
40 hp=29840 watts
I know P=W/t but what is W?
CORRECTION: that is supposed to be 15m/s NOT 15m/2
3.2 s
In the equation P = W/t, P represents power, W represents work, and t represents time. To find the value of W (work), we need to rearrange the formula.
W = P × t
In this case, you're given that the power is 29840 watts and you're looking for the work done over a specific time interval. However, we need a bit more information to determine the time it takes for the car to reach the given speed.
To find the time, we can make use of the formula for acceleration:
a = (v - u) / t
where:
a = acceleration,
v = final velocity, and
u = initial velocity.
Considering the car starts from rest, the initial velocity (u) is 0 m/s.
Given that the final velocity (v) is 15 m/s and the car's mass (m) is 850 kg, we can now solve for acceleration (a).
a = (15 m/s - 0 m/s) / t
a = (15 m/s) / t
Next, we want to find the time (t) it takes to reach this speed. We can rearrange the formula for acceleration to solve for time:
t = (15 m/s) / a
To calculate the acceleration, we need to use Newton's second law of motion:
F = m × a
where:
F = force, and
m = mass.
In this case, we'll assume the car is moving in a straight line, neglecting friction and any other external forces. Therefore, in the absence of friction, the force required to accelerate the car is equal to the gravitational force acting on it, given by:
F = m × g
where:
g = acceleration due to gravity (approximately 9.8 m/s^2).
F = (850 kg) × (9.8 m/s^2) = 8330 N
Now we can calculate the acceleration:
8330 N = (850 kg) × a
a = 9.8 m/s^2
Substituting the value of acceleration back into the equation for time:
t = (15 m/s) / (9.8 m/s^2)
Now, t = 1.53 seconds (rounded to two decimal places).
Finally, the work done to reach this speed can be calculated using:
W = P × t
W = (29840 watts) × (1.53 seconds)
After performing the multiplication, the work done by the 850 kg car to reach a speed of 15 m/s without considering friction is approximately 45650 joules (rounded to the nearest whole number).
Please note that this calculation neglects friction and assumes the car is accelerating in a straight line. The actual time taken in real-world scenarios would be different due to various factors like air resistance, rolling resistance, and other forces.
P= mas
here, m=mass
a=accleration
s=distance