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Multivariable Calculus

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Moderate

Compare Two Objects

MVCALC-V11NL3

Two objects move along the same smooth curve so that the velocity of the first object is given by the function ${\bf v}(t)$, and the velocity of the second object is given by the function $2{\bf v}(t)$.

The two objects start at the same point.

If the tangential and normal components of acceleration in a fixed moment $t$ are denoted by $a( T_1)$ and $a( N_1)$ for the first object, and by $a(T_2)$ and $a(N_2)$ for the second object, which of the following five statements is NOT always true?

A

At any given moment, the position vector of the second object is equal to twice the position vector of the first object.

B

$2a(N_1)=a( N_2)$

C

$2a(T_1)=a( T_2)$

D

$a(T_2)^2 + a( N_2)^2 = 4a(T_1)^2 + 4a( N_1)^2 $

E

At any given moment, the speed of the second object is twice the speed of the first object.