PARAMETRICS AND VECTORS - korpisworld
PARAMETRICS AND VECTORS
WORKSHEET 3
Work the following on notebook paper. Use your calculator only on problems 3-7.
1. The position of a particle at any time [pic] is given by [pic], [pic].
a. Find the magnitude of the velocity vector at [pic].
b. Set up an integral expression to find the total distance traveled by the particle from [pic]to [pic].
c. Find [pic] as a function of x.
d. At what time t I s the particle on the y-axis? Find the acceleration of the vector at this time.
2. An object moving along a curve in the xy-plane has position [pic] at time t with the velocity vector [pic]. At time [pic], the object is at [pic].
a. Find the position vector.
b. Write an equation for the line tangent to the curve when [pic].
c. Find the magnitude of the velocity vector when [pic].
d. At what time [pic] does the line tangent to the particle at [pic] have a slope of 12?
3. A particle moving along a curve in the xy-plane has position [pic], with [pic] and [pic], where [pic]. Find the velocity vector at the time when the particle’s vertical position is [pic].
4. A particle moving along a curve in the xy-plane has position [pic] at time t with [pic]. The derivative [pic] is not explicitly given. For any [pic], the line tangent to the curve at [pic] has a slope of [pic]. Find the acceleration vector of the object at time [pic].
5. An object moving along a curve in the xy-plane has position [pic] at time t with [pic] and [pic] for [pic]. At time [pic], the object is at the point [pic].
a. Find the equation of the tangent line to the curve at the point where [pic].
b. Find the speed of the object at [pic].
c. Find the total distance traveled by the object over the time interval [pic].
d. Find the position of the object at time [pic].
6. A particle moving along a curve in the xy-plane has position [pic] at time t with [pic] and [pic]. At time [pic], the particle is at the point [pic].
a. Find the acceleration vector for the particle at [pic].
b. Find the equation of the tangent line to the curve at the point where [pic].
c. Find the magnitude of the velocity vector at [pic].
d. Find the position of the particle at time [pic].
7. An object moving along a curve in the xy-plane has position [pic] at time t with [pic]. The derivative of [pic] is not explicitly given. At [pic], the object is at the point [pic].
a. Find the y-coordinate of the position at time [pic].
b. At time [pic], the value of [pic] is [pic]. Find the value of [pic] when [pic].
c. Find the speed of the object at time [pic].
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