Vector-Valued Functions (College Board AP® Calculus BC): Exam Questions

A particle moves in the -plane so that its position is given by the vector at time .

The acceleration vector of the particle is

A particle travels along a curve in the -plane such that its velocity vector is where . Its position vector at time is .

The position vector at time is

If is a vector-valued function defined by , then is

A particle travels along a curve in the -plane, where its acceleration vector is at time . The velocity vector at time is .

The velocity vector at time is

The position of a particle moving in the -plane is given by the vector where is time.

The speed of the particle at time is

A particle moves with a position vector of in the -plane, where time . The total distance traveled in the first four seconds is

The acceleration vector of a particle moving in the -plane is , where is time and the -axis points vertically upwards. At the beginning of its journey, time , the particle is at a position vector of moving with a speed of 1 in a direction that is vertically downwards.

The position vector of the particle at time is

A particle is moving in the -plane where the -axis is horizontal and increases towards the right. The position vector of the particle is where is time and .

For which of the following time intervals is the particle always moving towards the left?

The function is a vector-valued function with its second derivative defined by , where and are constants. It is known that and .

The value of is

A particle moves in the -plane such that, at time , its position vector is , where is an integer. If the acceleration vector at time is and the -component of the acceleration vector tends towards as , then