a 1000kg car is travelling with a speed of 33.3m/s2 when the driver saw an intersection 30m away. how much force is needed to stop the car right away?
Well, stopping a car right away is no small task! It's like asking a buffet enthusiast to suddenly stop devouring ice cream. But fear not, my friend, as I have the equation of motion up my clown sleeve to help us out. The force required to stop the car can be calculated using the equation: force = mass × acceleration.
Given that the mass (m) of the car is 1000 kg and the acceleration (a) is the negative of the initial velocity (v), we have a = -33.3 m/s². Plugging those values into the equation, we get:
Force = 1000 kg × (-33.3 m/s²)
And the answer, my inquisitive friend, is that approximately 33,300 Newtons of force are needed to stop that car right away. That's like giving an elephant a piggyback ride!
To determine the force needed to stop the car right away, we can use the formula:
Force = (mass of the car) × (change in velocity) / (time taken)
Given:
Mass of the car (m) = 1000 kg
Initial velocity (u) = 33.3 m/s
Final velocity (v) = 0 m/s (car needs to stop)
Distance traveled (s) = 30 m
First, we need to calculate the change in velocity:
Change in velocity (Δv) = Final velocity (v) - Initial velocity (u)
Δv = 0 m/s - 33.3 m/s
Δv = -33.3 m/s (negative sign indicating the direction opposite to the initial velocity)
Next, we can calculate the time taken (t) using the formula for constant acceleration:
s = (u + v) × t / 2
Rearranging the equation:
2s = (u + v) × t
Plugging in the values:
2(30 m) = (33.3 m/s + 0 m/s) × t
60 m = 33.3 m/s × t
t = 60 m / 33.3 m/s
t ≈ 1.801801802 seconds (rounded to 3 decimal places)
Finally, we can calculate the force:
Force = (mass of the car) × (change in velocity) / (time taken)
Force = 1000 kg × (-33.3 m/s) / 1.801801802 s
Force ≈ -18380.61882 N (rounded to 2 decimal places)
Since the force needed to stop the car is directed in the opposite direction of motion, the force is approximately 18380.62 N.
To calculate the force needed to stop the car right away, we can use Newton's second law of motion: force = mass × acceleration.
Given:
- Mass of the car (m) = 1000 kg
- Initial velocity of the car (u) = 33.3 m/s
- Final velocity of the car (v) = 0 m/s
- Distance to stop (s) = 30 m
First, we need to find the acceleration (a) using the kinematic equation:
v^2 = u^2 + 2as
Rearranging the equation, we have:
a = (v^2 - u^2) / (2s)
= (0 - 33.3^2) / (2 × 30)
= -3330.09 / 60
= -55.50 m/s^2
The acceleration is negative because it opposes the direction of motion, as we want to stop the car.
Now, we can calculate the force needed:
force = mass × acceleration
= 1000 kg × (-55.50 m/s^2)
= -55,500 N
Therefore, the force needed to stop the 1000 kg car right away is -55,500 Newtons, in the opposite direction of the car's motion.
Suspect speed is 33.3 m/s
average speed during stop = 33.3/2 =16.65
time to stop = t = 30/16.65 = 1.80 s
d = .5 a t^2
30 = .5 a 1.8^2
so
a = 18.5 m/s^2
so
F = m a = 1000*18.5 = 18,500 Newtons