A 5.0 kg model vehicle travelling at 14 m/s experiences a rocket boost of 85 N ( in the direction of motion) for 20 s
What is the resulting speed?
The answer is 350 but i don't know how to get to that answer
a = F/m = 85/5 = 17 m/s^2.
V = Vo + a*t = 14 + 17*20 = 354 m/s.
Well, let's crunch the numbers and see if we can figure it out together!
We have a model vehicle that initially is traveling at 14 m/s and experiences a rocket boost of 85 N in the direction of motion for 20 seconds.
To find the resulting speed, we can use the concept of impulse. Impulse is defined as the product of force and time.
The impulse, J, is given by the formula:
J = Δp = mΔv
Where:
J = impulse
Δp = change in momentum
m = mass of the vehicle
Δv = change in velocity
In this case, the force (85 N) is acting on the vehicle for 20 seconds. So, we can calculate the impulse:
J = FΔt = (85 N)(20 s) = 1700 N·s
The impulse is also equal to the change in momentum of the vehicle. Initially, the momentum is given by the mass (5.0 kg) times the initial velocity (14 m/s).
Initial momentum = (5.0 kg)(14 m/s) = 70 kg·m/s
The change in momentum is given by the difference between the final momentum and the initial momentum.
Δp = final momentum - initial momentum
Since we want to find the final velocity, let's rearrange the equation:
Final momentum = initial momentum + Δp
Final momentum = (5.0 kg)(14 m/s) + 1700 N·s = 70 kg·m/s + 1700 N·s
Now, let's plug in the values:
Final momentum = 70 kg·m/s + 1700 N·s = 770 kg·m/s
Finally, we divide the final momentum by the mass of the vehicle to find the resulting speed:
Resulting speed = Final momentum / mass
= 770 kg·m/s / 5.0 kg
= 154 m/s
Uh-oh, it seems like my calculations aren't adding up to the answer you provided. I'm sorry for not being able to help you get to the answer of 350 m/s. It's possible my clownish calculations took a wrong turn along the way. Let me know if there's anything else I can try to help you with!
To find the resulting speed of the vehicle, we can use 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 rocket boost is the net force acting on the vehicle.
First, let's calculate the acceleration of the vehicle using the formula:
Acceleration (a) = Net force (F) / Mass (m)
Using the given values, we have:
Acceleration (a) = 85 N / 5.0 kg
Acceleration (a) = 17 m/s^2
Next, we need to determine the change in velocity during the 20-second time period. The formula relating acceleration, initial velocity, and time is:
Change in velocity (Δv) = a × t
Using the given values, we have:
Change in velocity (Δv) = 17 m/s^2 × 20 s
Change in velocity (Δv) = 340 m/s
Finally, we find the resulting speed (v) by adding the change in velocity (Δv) to the initial velocity (14 m/s):
Resulting speed (v) = Initial velocity + Change in velocity
Resulting speed (v) = 14 m/s + 340 m/s
Resulting speed (v) = 354 m/s
Therefore, the resulting speed of the vehicle is 354 m/s, not 350 m/s as stated in the answer.
To find the resulting speed, we need to first calculate the change in momentum caused by the rocket boost. The change in momentum is equal to the product of the force and the time duration for which the force is applied.
Given that the force applied by the rocket boost is 85 N and the time duration is 20 seconds, we can calculate the change in momentum using the formula:
Change in momentum = Force × Time
Change in momentum = 85 N × 20 s
Change in momentum = 1700 N·s
Next, to find the resulting velocity, we need to divide the change in momentum by the mass of the vehicle:
Resulting velocity = Change in momentum / Mass
Resulting velocity = 1700 N·s / 5.0 kg
Resulting velocity = 340 m/s
Therefore, the resulting speed of the vehicle after the rocket boost is 340 m/s. It seems the answer given (350) might be a rounding error, as the exact calculation yields 340 m/s.