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Chapter 1: Q15DQ (page 263)

A net force of 4 N acts on an object initially at rest for0.25 s and gives it a final speed of 5 m/s. How could a net force of2 N produce the same final speed?

Short Answer

Expert verified

If 2N force is applied for 0.5s will produce the same final velocity.

Step by step solution

01

Momentum of a particle

The momentumP→of a particle is a vector quantity equal to the product of

the particle’s mass mand velocityv→ .

P→=mv→

For a constant force change in momentum.

∆p=F∆t

02

Discussion

The velocity of the object is proportional to its momentum.

So, for the same final velocity, the final momentum will be the same.

As we know for a constant force, the change in momentum=F∆t

Therefore, the final momentum will be the same, ifF∆t is the same in both cases.

F1∆t1=F2∆t2

As we know,

F1=4N1∆t1=0.25s

And

F2=2N

Substituting the values

4N0.25s=2N∆t2∆t2=0.5s

Therefore, if 2N force is applied for 0.5s will give the same final velocity to the object.

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