本题目来源于试卷: 2007美国US F=MA物理竞赛，类别为 美国F=MA物理竞赛
[单选题]
At time $t=0$ a drag racer starts from rest at the origin and moves along a straight line with velocity given by $v=5t^{2}$, where $v$ is in $m/s$ and $t$ in $s$. The expression for the displacement of the car from $t=0$ to time $t$ is
A. $5t^{3}$
B. $5t^{3}/3$
C. $10t$
D. $15t^{2}$
E. $5t/2$
参考答案: B
本题详细解析:
Displacement $x$ is the integral of velocity $v(t)$ with respect to time $t$.
$x(t) = \int v(t) dt = \int 5t^2 dt$.
Using the power rule for integration: $x(t) = 5 \left(\frac{t^3}{3}\right) + C$.
Since the racer starts from the origin at $t=0$, $x(0) = 0$, which means the constant of integration $C=0$.
Therefore, the displacement is $x(t) = 5t^3/3$.
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