AP 微积分 BC

Question

if a particle moves along a curve with constant speed then
A the magnitude of its acceleration must equal 0
B the direction of accleration must be constant
C the curve along which the particle moves must be a straight line
D its velocity and acceleration vectors must be perpendicular
E the curve along which the particle moves must be a circle

答案是d
但我几个选项为什么不选都不是很清楚
能每个选项都能分析一下吗

谢谢

Answer 1

if a particle moves along a curve with constant speed then

A the magnitude of its acceleration must equal 0
答：错。
质子沿曲线做匀速率运动，虽然是匀速率，但加速度是矢量vector，
只要沿曲线运动，就一定有加速度，所以加速度不为0。

B the direction of accleration must be constant
答：错。
做匀速率圆周运动的质点，加速度的方向永远指向圆心，它是时时
刻刻在改变的。沿曲线运动质点的加速度方法，时时刻刻指向曲线
上的点所对应的曲率圆的圆心，所以，加速度的方向时刻在改变。

C the curve along which the particle moves must be a straight line
答：错。
这句话是无厘头话，前后矛盾，是出题人欠考虑的话。

D its velocity and acceleration vectors must be perpendicular
答：对。
沿曲线运动，是tangential motion，加速度是centripetal，指向曲率
圆的圆心，它们perpendicular each other。

E the curve along which the particle moves must be a circle

答：错。
这也是无厘头的话，沿曲线匀速率运动，不一定曲线一定是circle。