You accelerate your 1500 Kg car from 2 m/s to 12 m/s in 2 seconds. How do you determine
the cars acceleration
initial momentum
final momentum
change in momentum
the force required to do this?
a = change in v / change in time
= (12-2)/2 = 5 m/s^2
m Vi = 1500 * 2 = 3000 kg m/s
m Vf = 1500 * 12 = 18,000 kg m/s
18,000 - 3000 = 15,000 kg m/s
F = rate of change of momentum
= m a
do both ways
F = 15,000/2 = 7,500 N
or
F = 1500 * 5 = 7,500 N
remarkable LOL
Now
What Newton actually said was
F = rate of change of momentum
but
that is d/dt ( m v)
BUT
usually m is constant
so
we say F = m dv/dt but dv/dt is a
so F = m a
If you are doing a problem like a rocket expelling fuel where the mass is not constant, it helps to remember that F = d/dt (m v)
:)
To determine the car's acceleration, you can use the formula:
Acceleration (a) = (Final velocity (v) - Initial velocity (u)) / Time (t)
In this case, the final velocity (v) is 12 m/s, the initial velocity (u) is 2 m/s, and the time (t) is 2 seconds. Plugging these values into the formula:
Acceleration (a) = (12 m/s - 2 m/s) / 2 s
Acceleration (a) = 10 m/s^2
The car's acceleration is 10 m/s^2.
To determine the car's initial momentum, you can use the formula:
Initial Momentum (p) = Mass (m) × Initial velocity (u)
Here, the mass (m) of the car is given as 1500 kg, and the initial velocity (u) is 2 m/s. Plugging these values into the formula:
Initial Momentum (p) = 1500 kg × 2 m/s
Initial Momentum (p) = 3000 kg·m/s
The car's initial momentum is 3000 kg·m/s.
To determine the car's final momentum, you can use the formula:
Final Momentum (p) = Mass (m) × Final velocity (v)
The mass (m) of the car is 1500 kg, and the final velocity (v) is 12 m/s. Plugging these values into the formula:
Final Momentum (p) = 1500 kg × 12 m/s
Final Momentum (p) = 18000 kg·m/s
The car's final momentum is 18000 kg·m/s.
The change in momentum is the difference between the final and initial momentum:
Change in Momentum (Δp) = Final Momentum (p) - Initial Momentum (p)
Plugging in the values we calculated:
Change in Momentum (Δp) = 18000 kg·m/s - 3000 kg·m/s
Change in Momentum (Δp) = 15000 kg·m/s
The change in momentum is 15000 kg·m/s.
To calculate the force required to accelerate the car, you can use Newton's second law of motion:
Force (F) = Mass (m) × Acceleration (a)
In this case, the mass (m) of the car is 1500 kg, and the acceleration (a) is 10 m/s^2. Plugging these values into the formula:
Force (F) = 1500 kg × 10 m/s^2
Force (F) = 15000 N
The force required to accelerate the car is 15000 Newtons (N).