A force of 16 N pushes on a 8 kg cart. How fast will the cart be going when it has traveled 2m?
the cart's acceleration is ... a = f / m = 16 / 8
distance = 1/2 a t^2
... find the time to travel 2 m
velocity = acceleration * time
thank u so much.
To determine the speed of an object, you can use the equation:
Speed = Distance ÷ Time
In this case, we need to find the speed of the cart when it has traveled 2m. However, we do not have the time given. To solve this, we need to calculate the time taken using the information given.
To find the time, we can use the formula:
Force = Mass × Acceleration
Rearranging this formula to solve for acceleration:
Acceleration = Force ÷ Mass
Given that the force acting on the cart is 16 N and the mass of the cart is 8 kg, we can calculate the acceleration:
Acceleration = 16 N ÷ 8 kg = 2 m/s^2
Now, we can use a different formula to find the time:
Time = Final Velocity ÷ Acceleration
Since the initial velocity is not given, we assume it to be zero. Thus, the final velocity is the speed we are looking for. Substituting the values:
Time = Speed ÷ 2 m/s^2
We do not know the value of time, but we can calculate it using the formula for distance:
Distance = Initial Velocity × Time + (1/2) × Acceleration × Time^2
Again, assuming the initial velocity is zero, the equation simplifies to:
Distance = (1/2) × Acceleration × Time^2
Rearranging this equation to solve for time:
Time = √(2 × Distance ÷ Acceleration)
Substituting the given distance of 2m and the calculated acceleration of 2 m/s^2:
Time = √(2 × 2m ÷ 2 m/s^2)
Calculating this:
Time = √(2 s^2) = √2 s ≈ 1.41 s
Now that we have the time, we can find the speed:
Speed = Distance ÷ Time
Substituting the given distance of 2m and the calculated time of 1.41s:
Speed = 2m ÷ 1.41s ≈ 1.42 m/s
Therefore, when the cart has traveled 2m, it will have a speed of approximately 1.42 m/s.