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sergejj [24]
3 years ago
9

An object moves with velocity v(t)=t^2-8t+7

Physics
1 answer:
solong [7]3 years ago
6 0
<span>a) write a polynomial expression for the position of the particle at any time t greater or equal to zero. 
</span>Position is found by integrating velocity: 

<span>s(t) = (t^3)/3 - 4t^2 + 7t + c 
</span>where c is a constant corresponding to the position at t=0. <span>

b) at what time(s) is the particle changing direction
</span>the particle changes direction whenever the velocity is zero; the velocity function equals 

<span>(t-1)(t-7) a difference of squares so the zeros are 1 and 7, it changes direction at 1 second and 7 seconds. </span><span>

c) find the total distance traveled by the particle from t=0 and t=4
</span><span>s(0) = c
s(1) = 8/3 + c
s(4) = 64/3 - 64 + 28 + c. 
</span>
from 0 to 1 the particle travels 8/3 units. From 1 to 4 it travels -(64/3 - 36 - 8/3) = (-(56/3 - 108/3)) 
<span>=-(-52/3) = 52/3 units 
</span>
<span>so in total it travels 52/3 + 8/3 =20 units</span>
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