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Q. 40

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Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
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Short Answer

A particle’s velocity is described by the function vx = kt 2 m/s, where k is a constant and t is in s. The particle’s position at t0 = 0 s is x0 = - 9.0 m. At t1 = 3.0 s, the particle is at x1 = 9.0 m. Determine the value of the constant k. Be sure to include the proper units

The value of constant k is 2.

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Step by Step Solution

Given information

The velocity of a particle is given by a function vx=kt2 ms.

The position of the particle at t0=0s is x0=-9.0 m.

The position of the particle at t1=3.0s is x1=9.0m.

The value of constant k.

The position of a particle is given by

xf=x0+t0tfvxdt

here,

role="math" localid="1648490216091" x1=x0+t0t1vxdt=x0+t0t1kt2dt=x0+13kt3t0t1=x0+13kt13-13kt03

Substitute known values

9=-9+13k33-13k039=-9+9k9k=18k=2

Therefore, the value of constant k is 2.

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