An object moving in a straight line has velocity $v ( t ) = t e ^ { - \sqrt { t } }$ meters per second. Is it true that in the first 4 seconds the object will have travelled $4 e ^ { 2 } + 12$ meters?

Question

Quizplus · Accepted Answer

The distance traveled is the integral of velocity with respect to time. So, the distance traveled in the first 4 seconds is:$$\int_0^4 t e ^ { - \sqrt { t } } dt = \left [ -2 e ^ { - \sqrt { t } } \right ]_0^4 = -2 e ^ { - 2 } + 2 = 4 e ^ { 2 } + 12$$

An Object Moving in a Straight Line Has Velocity v(t)=te−tv ( t ) = t e ^ { - \sqrt { t } }v(t)=te−t​

An Object Moving in a Straight Line Has Velocity $v ( t ) = t e ^ { - \sqrt { t } }$