Question

plotting a graph for momentum on the X-axis and time on Y-axis, slope of momentum time graph gives a) impulsive force, b) acceleration, c) force, d) rate of force​

Answer 1

Answer:

Force = F

Explanation:

Let

Force = F

Momentum = M

Time = T

IF

Momentum is alone Y-axis

Time is alone X-axis

Then

Small change on Y-axis = Δy = change in momentum = Δp

Small change on X-axis = Δx = change in time = Δt

By definition of slope of graph

Slope of Momentum time graph =  Δy /  Δx =  Δp / Δt

we know that

IF

m = mass of body

Vi = initial velocity of body

Vf = final velocity of body

then

Δp = m(Vf - Vi)

So

Slope of Momentum-time graph =  Δy /  Δx =  m (Vf- Vi) / Δt

And we also know that

Acceleration of body = α = (Vf- Vi) / Δt

Therefore

Slope of Momentum-time graph =  m α

Now using second law of newton

F = m α  

We get

Slope of Momentum-time graph =  F = force.

Answer 2

Plotting a graph for momentum on the X-axis and time on Y-axis, slope of momentum time graph gives c) force.

• The slope of the momentum-time graph is given as,
•  $\dfrac{\Delta y}{\Delta x} = \dfrac{\Delta p}{\Delta t} = m \times \dfrac{(v_f - v_i)}{t }$
• Where, m = mass of the object, vf = final velocity, vi = initial velocity
• $\dfrac{\Delta y}{\Delta x} = m \times a$......(1)
• Force equation is given by,
• F = m × a ......(2)
• Comparing equations (1) and (2),
•  $\dfrac{\Delta y}{\Delta x} = F$
• Where,   Δy/Δx represents the slope momentum-time graph.
• Thus, plotting a graph for momentum on the Y-axis and time on X-axis. the slope of the momentum-time graph gives force.