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Chapter 2: Q. .31 (page 60)

FIGURE EX2.31 shows the acceleration-versus-time graph of a particle moving along the x-axis. Its initial velocity is v0x = 8.0 m/s at t0 = 0 s. What is the particle鈥檚 velocity at t = 4.0 s?

Short Answer

Expert verified

The velocity of a particle at t=4sis 16 m s-1.

Step by step solution

01

Given information

Initial velocity of a particle, v0=8.0ms

Initial time,t0=0s

02

The velocity of a particle.

The change in velocity of a particle 鈭�v=vf-v0between t0and tfis the area under the curve from t0=0sto tf=4s. In this case, the curve is a triangle.

Thus, the area of a triangle is

鈭�v=area of the triangle between t0=0sand tf=4s.

鈭�v=12脳4s脳4ms2=8ms

Now,

The velocity of a particle at tf=4sis given by

vf=v0+area under the acceleration curve axbetween t0and tf

localid="1648468773258" role="math" vf=8.0ms+8ms=16m/s

Therefore, the velocity of a particle at t=4sis 16 m s-1. .

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