AP Calculus ABhardmcq1 pt

A particle moves along a line with velocity $v(t)=t^3-4t$ for $0\le t\le 3$ . What is the total distance traveled by the particle?

\frac{9}{4}

\frac{41}{4}

4

\frac{25}{4}

Explanation

Core Concept

The velocity is negative on $(0,2)$ and positive on $(2,3)$ . The distance is $\int_0^2(4t-t^3)\,dt+\int_2^3(t^3-4t)\,dt=4+\frac{25}{4}=\frac{41}{4}$ .

Correct Answer

B $\frac{41}{4}$

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Practice Unit 8: Applications of Integration Questions →

A particle moves along a line with velocity v(t)=t3−4tv(t)=t^3-4tv(t)=t3−4t for 0≤t≤30\le t\le 30≤t≤3. What is the total distance traveled by the particle?

Explanation

Core Concept

Correct Answer

More Unit 8: Applications of Integration practice questions

A particle moves along a line with velocity $v(t)=t^3-4t$ for $0\le t\le 3$ . What is the total distance traveled by the particle?