A particle that moves along a straight line has velocity v(t)=(t^2)e^(-2t) meters per second after t seconds.?
How many meters will it travel during the first "t" seconds?
To find how many meters a particle will travel during the first "t" seconds, we need to calculate the definite integral of the velocity function over the interval from 0 to "t".
The given velocity function is v(t) = (t^2)e^(-2t) meters per second.
To find the displacement, we integrate the velocity function with respect to time over the interval [0, t].
∫(0 to t) (t^2)e^(-2t) dt
To find this integral, we can use integration techniques such as integration by parts or substitution. However, the integration of this function can be quite complex.
Alternatively, we can use software or online tools to evaluate the integral for us. Numerous online tools and software, like Wolfram Alpha or Mathematica, can perform this integral and provide the result.
Once we have the result, the value obtained will represent the displacement of the particle during the first "t" seconds.