Suppose a particle moves along a straight line with velocity v(t)=t2e−2tv(t)=t2e−2t meters per second after t seconds. how many meters has it traveled during the first t seconds?

For a particle moving along a straight line with a velocity the distance traveled in meters is

Let us recall that;

v = ds/dt hence;

s =

Within the first t seconds;

s =

Hence, for

s =

Integrating by parts;

Note that;

u =

du =

dv =

v =

Substituting;

Integrating by parts, we have the result;

meters

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Explanation:

It is given that,

Velocity of the particle moving in straight line is :

We need to find the distance (x)  traveled by the particle during the first t seconds. It is given by :

Using by parts integration, we get the value of x as :

Hence, this is the required solution.

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