A force of -9000N is used to stop a 1500 kg car traveling at 20m/s. What braking distance is needed to bring the car to a halt?
Vf^2=Vi^2 + 2ad
but a= force/mass
solve for distance d
To find the braking distance needed to bring the car to a halt, we can use the equation for force:
Force = mass × acceleration
In this case, the force exerted on the car is -9000N (negative because it opposes the car's motion), and the mass of the car is 1500 kg. We need to determine the acceleration.
To find the acceleration, we can use the equation for acceleration:
acceleration = change in velocity / time
In this case, the initial velocity of the car is 20 m/s (given in the question), and the final velocity is 0 m/s (since the car comes to a halt). Therefore:
acceleration = (0 m/s - 20 m/s) / time
Since the car comes to a halt, the final velocity is 0 m/s. And we know that the initial velocity is 20 m/s. Rearranging the equation:
time = change in velocity / acceleration
Substituting the values:
time = (0 m/s - 20 m/s) / acceleration
Now we can substitute the value of the force into the equation for force:
-9000N = 1500 kg × acceleration
Solving for acceleration:
acceleration = -9000N / 1500 kg
acceleration = -6 m/s²
Now we can substitute the value of acceleration into the equation for time:
time = (0 m/s - 20 m/s) / -6 m/s²
time = 20 s
Finally, to find the braking distance, we can use the equation for distance:
distance = 1/2 x acceleration x time²
Substituting the values:
distance = 1/2 x -6 m/s² x (20 s)²
distance = -6 m/s² x 400 s²
distance = -2400 m²
Since distance cannot be negative, we take the absolute value:
distance = 2400 m
Therefore, the braking distance needed to bring the car to a halt is 2400 meters.