# What is the speed of the particle?

##
A particle moves with its position given by x=cos(4t) and y=sin(t), where positions are given in feet from the origin and time t is in seconds.

A particle moves with its position given by x=cos(4t) and y=sin(t), where positions are given in feet from the origin and time t is in seconds.

Oh. Oh. Oh. I got this one.

By taking the first derivative of the x and y functions, you can find the components, which can be added up to find the velocity:

Your velocity, then, is a vector with the previously mentioned components.

The Pythagorean theorem can be used to determine the speed, which is the vector's magnitude:

Though there might be a more ingenious way to make this even simpler, maybe this will do.

By signing up, you agree to our Terms of Service and Privacy Policy

To determine the speed of a particle, we need information about its velocity, which is a vector quantity representing both speed and direction. If you provide the velocity vector of the particle, I can calculate its speed by finding the magnitude of the velocity vector, which represents the particle's speed without regard to direction. Please provide the velocity vector of the particle in order to proceed with the calculation.

By signing up, you agree to our Terms of Service and Privacy Policy

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- If a projectile is shot at an angle of #pi/6# and at a velocity of #23 m/s#, when will it reach its maximum height??
- The position of an object moving along a line is given by #p(t) = 2t^3 - 5t^2 +2#. What is the speed of the object at #t = 2 #?
- An object's two dimensional velocity is given by #v(t) = ( 3t^2 - 2t , 1- 3t )#. What is the object's rate and direction of acceleration at #t=5 #?
- An object is at rest at #(8 ,7 ,3 )# and constantly accelerates at a rate of #1/4 m/s^2# as it moves to point B. If point B is at #(1 ,3 ,4 )#, how long will it take for the object to reach point B? Assume that all coordinates are in meters.
- An electron with initial velocity v0 = 1.10 × 10^5 m/s enters a region 1.0 cm long where it is electrically accelerated (see the figure). It emerges with velocity v = 5.37 × 10^6 m/s. What is its acceleration, assumed constant?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7