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Chapter 2: Q. 40 (page 61)

A particle鈥檚 velocity is described by the function vx = kt 2 m/s, where k is a constant and t is in s. The particle鈥檚 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

Short Answer

Expert verified

The value of constantkis 2.

Step by step solution

01

Given information

The velocity of a particle is given by a function vx=kt2ms.

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

The position of the particle att1=3.0sisx1=9.0m.

02

The value of constant k.

The position of a particle is given by

xf=x0+鈭�t0tfvxdt

here,

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

Substitute known values

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

Therefore, the value of constantkis 2.

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Careful measurements have been made of Olympic sprinters in the 100 meter dash. A simple but reasonably accurate model is that a sprinter accelerates at 3.6 m/s2 for 313s, then runs at constant velocity to the finish line.

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