a math question, the velocity function is v(t) = 80e^(-0.1t), how far does an object go in 20 seconds?

Answer 1

distance=integral(v(t)dt from 0 to 20)
=integral(80e^(-0.1t)dt from 0 to 20)
=(-800e^(-0.1*20))
-(-800e^(-0.1*0))
=-800e^(-2)+800
=-800e^(-2)+800
~691.7

Answer 2

Syggestion:I suppose the distance is the area under the graph of v(t) ;upper limit 20 sec and lower limit 0 sec;
find area by integrating the given function and then apply the limits to get the numerical value;

Answer 3

actually to answer this question you must integrate the function since distance is the antiderivative of velocity. Therefore the anyiderivative becomes d(t)=-800*e^(-.1t)
This must be evaluated as d(20)-d(0). With thi i get 691.74 and then whatever the correct corresponding units are.

Answer 4

ds/dt = v(t) = 80 e^(-.1t)
s = 80 integ [e^(-.1t )]dt
s = 80 [-e^(-.1t) + C)
when t=0 , s=0 so 0 = 80(-1 +C) --> C = 1
s = 80(-e^(-.1t) +1)
s = 80(-e^(-.1(20))+1)
s = 80 (-e^-2+1) = 69.17 units

Answer 5

take the derivative of the function and then plug in 20 for t.

ends up being about -1.08 m (if that's your unit)