3某物体在力F(x)=15-3x2(力的单位:N,位移的单位:m)的作用下沿与力F(x)成30°角的方向由x=1 m直线运动到x=2 m处,作用力F(x)所做的功W为(　　)

A.√3 J B.2√3 J C.4√3 J D.√3/2 J

解析W=∫_1^2▒ F(x)cos 30°dx=√3/2 ∫_1^2▒ (15-3x2)dx=√3/2(15x-x3)"|" _1^2=√3/2[(30-8)-(15-1)]=4√3(J).

答案C

某物体做变速直线运动,其v-t曲线如图所示,该物体在1/2 6 s间运动的路程s为.

解析v(t)={■(2t"," 0≤t≤1"," @2"," 1

　　由变速直线运动的路程公式,可得所求路程

　　s=∫_(1/2)^6▒ v(t)dt=∫_(1/2)^1▒ 2tdt+∫_1^3▒ 2dt+∫_3^6▒ (1/3 t+1)dt

　　=t2"|" _(1/2)^1+2t"|" _1^3+(1/6 t^2+t) "|" _3^6=49/4(m).

　　所以物体在1/2 6 s间运动的路程是49/4 m.

答案49/4 m

5一辆汽车做变速直线运动,其速度函数v=v(t)={■(3t^2 "," t"∈[" 0"," 2"]," @2t+4"," t"∈(" 2"," 10"]," @24"," t"∈(" 10"," 58"]," @"-" 6"(" t"-" 58")" ^2+24"," t"∈(" 58"," 60"]." )┤

(其中时间t的单位:s,速度v的单位:m/s)

(1)求汽车前2 s经过的路程s1;

(2)求汽车前30 s经过的路程s2;

(3)求汽车1 min内经过的路程s.

分析先根据题意求出各时间段上的速度函数,再在对应时间段上求定积分.

解(1)当0≤t≤2时,v=3t2.

　　则s1=∫_0^2▒ 3t2dt=t3"|" _0^2=8(m).

　　(2)当0≤t≤2时,v=3t2;

当2