The velocity of a particle moving along the x-axis is given by v(t) = tsin(t^2). Find the total distance traveled from t = 0 to t = 3. A) 1.0 B) 1.5 C) 2.0 D) 2.5 E) 3.0 ?
It says you can use a calculator, so I used a calculator to calculate this integral:
#\int_0^3|tsin(t^2)|dt#
and I get approximately 2.961, which isn't one of the answer choices.
Am I doing something wrong or am I just supposed to round up to 3.0.
It says you can use a calculator, so I used a calculator to calculate this integral:
and I get approximately 2.961, which isn't one of the answer choices.
Am I doing something wrong or am I just supposed to round up to 3.0.
1 Answer
Aug 16, 2017
E.
Explanation:
In short, your answer was correct, because position is the integral of velocity, and the distance traveled is always positive, so we take the absolute value of the integral:
#int_0^3 |tsin(t^2)|color(white)(l)dt = 2.96color(white)(l)"m" ~~ color(red)(ulbar(|stackrel(" ")(" "3.0color(white)(l)"m"" ")|)#
All the answers are given with one decimal place, so it would be conventional to round this to one decimal place, making option E the correct choice.
