A remote-controlled toy car of mass 2.2 kg starts from rest at the origin at t = 0 and moves in the positive direction of an x axis. The net force on the car as a function of time is given by the figure. (a) What is the time rate of change of the momentum of the car at t = 3.0 s? (b) What is the momentum of the car at t = 3.0 s?
at t= 3.0 s for part a the force value is 4 N which is also similar for part b in order to calculate the momentum please give me your answers with units.
i have known the answer in part a which is 4N but in part b.. ive done substituting those values in the formula of impulse then i get 1.3333... so on is it right?? please help
To find the time rate of change of momentum (part a), you can use Newton's second law, which states that force is equal to the rate of change of momentum:
Force = Rate of change of momentum
In equation form, this can be written as:
F = dp/dt
where F is the force acting on the object, dp/dt is the time rate of change of momentum, and p is the momentum of the car.
Since the force is given as 4 N at t = 3.0 s, we can substitute this value into the equation to find the time rate of change of momentum:
4 N = dp/dt
Therefore, the time rate of change of momentum at t = 3.0 s is 4 kg·m/s.
Now, to find the momentum of the car at t = 3.0 s (part b), you can integrate the force function with respect to time to find the change in momentum, and then add this change to the initial momentum of the car.
Since the force is constant at 4 N between t = 0 and t = 3.0 s, the change in momentum can be calculated using the impulse formula:
Impulse = Force * Time
The impulse is equal to the change in momentum, so we have:
Impulse = Δp = Force * Time
Substituting the values:
Impulse = Δp = 4 N * 3.0 s
Impulse = Δp = 12 N·s
Finally, to find the momentum at t = 3.0 s, you need to add the impulse to the initial momentum of the car, which is zero because it starts from rest:
Momentum at t = 3.0 s = Initial momentum + Impulse
Momentum at t = 3.0 s = 0 + 12 N·s
Therefore, the momentum of the car at t = 3.0 s is 12 kg·m/s.