a. Starting from rest, what is its speed after 2.0 s?b. How much distance did it...

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2. A motorcycle accelerates at a constant acceleration of 3.0 m/s2/
a. Starting from rest, what is its speed after 2.0 s?

b. How much distance did it travel at this time?

c. How much distance did it travel in the time interval from 2.0 s to 5.0 s?

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kharmsorz

Verified answer

Answer:

The motorcycle starts at rest, so $v_{0x}=0\:\textrm{m/s}$ .

a) We solve for the acceleration:

$v_{x}=v_{0x}+a_{x}t\\v_{x}=0+a_{x}t\\v_{x}=a_{x}t=(3.0\:\textrm{m/s}^2)(2.0s)=6\:\textrm{m/s}$

b) We solve for the distance:

$\Delta x=v_{0x}t+\dfrac{1}{2}a_{x}t^2\\\Delta x=0+\dfrac{1}{2}a_{x}t^2\\\\\Delta x=0+\dfrac{1}{2}(3.0\:\textrm{m/s}^2)(2.0\:\textrm{s})^2\\\\\Delta x= 6\:\textrm{m}$

c) We solve for the distance at the given time interval:

$\Delta x=v_{0x}\Delta t+\dfrac{1}{2}a_{x}(\Delta t)^2\\\Delta x=0+\dfrac{1}{2}a_{x}(\Delta t)^2\\\\\Delta x=0+\dfrac{1}{2}(3.0\:\textrm{m/s}^2)(5.0\:\textrm{s}-2.0\:\textrm{s})^2\\\\\Delta x= 13.5\:\textrm{m}$

kylesmika61 Thank you so much!

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