How long will it take a 2.30 x 10^3 kg truck to go from 22.2 m/s to a complete stop if acted on by a force of -1.26 x 10^4 N? what would be its stopping distance?
F*time=mass*changeinvelocity
solve for time.
for distance...
1/2 m vi^2= force*distance solve for distance.
To find the time it takes for the truck to come to a complete stop, we can use the formula:
Δv = (F / m) * t
Where:
Δv is the change in velocity (22.2 m/s - 0 m/s = 22.2 m/s),
F is the force acting on the truck (-1.26 x 10^4 N),
m is the mass of the truck (2.30 x 10^3 kg),
and t is the time.
Rearranging the formula, we have:
t = Δv / (F / m)
Substituting the given values:
t = 22.2 m/s / (-1.26 x 10^4 N / 2.30 x 10^3 kg)
Calculating the expression inside the parentheses:
t = 22.2 m/s / (-1.26 x 10^4 N / 2.30 x 10^3 kg) ≈ 0.405 seconds
So, it will take approximately 0.405 seconds for the truck to come to a complete stop.
To find the stopping distance, we can use the equation:
d = (1/2) * a * t^2
Where:
d is the stopping distance,
a is the acceleration, and
t is the time.
The acceleration (a) can be calculated using Newton's second law:
a = F / m
Substituting the given values:
a = (-1.26 x 10^4 N) / (2.30 x 10^3 kg)
Calculating the acceleration:
a = -5.478 x 10^0 m/s^2
Now, substituting the values of a and t into the equation for stopping distance:
d = (1/2) * (-5.478 x 10^0 m/s^2) * (0.405 s)^2
Calculating the stopping distance:
d = (1/2) * (-5.478 x 10^0 m/s^2) * (0.405 s)^2 ≈ 0.446 meters
Therefore, the stopping distance of the truck would be approximately 0.446 meters.
To calculate the time it takes for the truck to come to a complete stop, we need to apply Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration. In this case, the net force is given as -1.26 x 10^4 N (negative since it opposes the truck's motion), and the mass of the truck is 2.30 x 10^3 kg.
First, we need to find the acceleration of the truck. Rearranging the equation, we have:
Net force = mass × acceleration
=> acceleration = Net force / mass
Plugging in the given values, we get:
acceleration = (-1.26 x 10^4 N) / (2.30 x 10^3 kg)
Next, we can calculate the time it takes for the truck to stop by using the equation:
acceleration = change in velocity / time
Since the truck starts from a velocity of 22.2 m/s and comes to a complete stop (0 m/s), the change in velocity is:
change in velocity = final velocity - initial velocity = 0 - 22.2 m/s
Plugging in the values we calculated earlier:
(-1.26 x 10^4 N) / (2.30 x 10^3 kg) = (0 - 22.2 m/s) / time
We can rearrange this equation to solve for time:
time = (2.30 x 10^3 kg) × (0 - 22.2 m/s) / (-1.26 x 10^4 N)
Now, we can calculate the time it takes for the truck to stop by substituting the given values into the equation:
time = (2.30 x 10^3 kg) × (0 - 22.2 m/s) / (-1.26 x 10^4 N)
Next, let's calculate the stopping distance. The stopping distance is the distance the truck travels during the time it takes to come to a complete stop. We can use the equation:
stopping distance = initial velocity × time + (1/2) × acceleration × time^2
Plugging in the values we know:
stopping distance = 22.2 m/s × time + (1/2) × acceleration × time^2
Substituting the value of time we previously calculated:
stopping distance = 22.2 m/s × [(2.30 x 10^3 kg) × (0 - 22.2 m/s) / (-1.26 x 10^4 N)] + (1/2) × acceleration × [(2.30 x 10^3 kg) × (0 - 22.2 m/s) / (-1.26 x 10^4 N)]^2
Evaluating this equation will give us the stopping distance of the truck.