The position (x)-time (t) graph for a particle of mass 1 kg moving x- axis is shown in figure. Find impulse on particle at $t = 4 s .$

Question

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Answer 1

Velocity before $t = 4 s e c o n d$ is slope of $x - t$ graph which is $Δ x / Δ t = (x_{2} - x_{1}) / (t_{2} - t_{1}) (20 - 0) / (4 - 0) = 5 m / s$

Velocity after $t = 4 s e c o n d$ is slope after $t = 4 s e c o n d$ which is $(0 - 20) / (8 - 4) = - 5 m / s$
Change in velocity $= - 5 - (5) = - 10 m / s$ so change in momentum will be mass multiplied by change in velocity, i.e. $1 \times (- 10) = - 10 K g m / s$ which is also called impulse.

Answer 2

Velocity before

t = 4 s e c o n d

is slope of

x - t

graph which is

Δ x / Δ t = (x_{2} - x_{1}) / (t_{2} - t_{1}) (20 - 0) / (4 - 0) = 5 m / s

Velocity after

t = 4 s e c o n d

is slope after

t = 4 s e c o n d

which is

(0 - 20) / (8 - 4) = - 5 m / s

Change in velocity

= - 5 - (5) = - 10 m / s

so change in momentum will be mass multiplied by change in velocity, i.e.

1 \times (- 10) = - 10 K g m / s

which is also called impulse.

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