The particle has
and
, and is undergoing a constant acceleration of
.
This means its position at time
is given by the vector function,

![\implies\vec r(t)=\left[4\,\mathrm m+\left(2\dfrac{\rm m}{\rm s}\right)t-\left(1\dfrac{\rm m}{\mathrm s^2}\right)t^2\right]\,\vec\imath-\left(1\dfrac{\rm m}{\mathrm s^2}\right)t^2\,\vec\jmath](https://tex.z-dn.net/?f=%5Cimplies%5Cvec%20r%28t%29%3D%5Cleft%5B4%5C%2C%5Cmathrm%20m%2B%5Cleft%282%5Cdfrac%7B%5Crm%20m%7D%7B%5Crm%20s%7D%5Cright%29t-%5Cleft%281%5Cdfrac%7B%5Crm%20m%7D%7B%5Cmathrm%20s%5E2%7D%5Cright%29t%5E2%5Cright%5D%5C%2C%5Cvec%5Cimath-%5Cleft%281%5Cdfrac%7B%5Crm%20m%7D%7B%5Cmathrm%20s%5E2%7D%5Cright%29t%5E2%5C%2C%5Cvec%5Cjmath)
The particle crosses the x-axis when the
component is 0 for some time
, so we solve:




The negative square root introduces a negative solution that we throw out, leaving us with
or about 3.24 seconds after it starts moving.
Answer:
a) 2.933 m
b) 4.534 m
Explanation:
We're given the equation
v(t) = -0.4t² + 2t
If we're to find the distance, then we'd have to integrate the velocity, since integration of velocity gives distance, just as differentiation of distance gives velocity.
See attachment for the calculations
The conclusion of the attachment will be
7.467 - 2.933 and that is 4.534 m
Thus, The distance it travels in the second 2 sec is 4.534 m
Gas because that’s what the periodic table says
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