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An object with a mass of 1.5 kg changes its velocity from +15 m/s to +22 m/s during a time interval of 3.5 seconds. What impulse was delivered to the object?

Verified Answer :

AL2006

Momentum = (mass) x (speed).

Original momentum = (1.5 kg) x (15 m/s)  =  22.5 kg-m/s

New momentum  =  (1.5 kg) x (22 m/s)  =  33 kg-m/s .

The change in momentum is  (33 - 22.5) = +10.5 kg-m/s.

The change in the object's momentum is identical to
the impulse delivered to it.

Answer : Impulse, I = 10.5 kg-m/s

Explanation :

It is given that,

Mass of an object, m = 1.5 kg

Initial velocity of the object, u = 15 m/s

Final velocity of the object, v = 22 m/s

Time duration, t = 3.5 s

We know that the impulse is equal to the change in momentum of an object.

i.e.

\(\because F=ma\)

\(a=\dfrac{\Delta v}{\Delta t}\)

\(I=F.\Delta t=m.\Delta v\)

\(I=1.5\ kg(22\ m/s-15\ m/s)\)

\(I=10.5\ kg\ m/s\)

Hence, the impulse delivered to the object is 10.5 kg-m/s.

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