# An object's two dimensional velocity is given by #v(t) = ( sqrt(t-2)-2t , t^2)#. What is the object's rate and direction of acceleration at #t=3 #?

2nd quandrant (negative x and positive y)

3 (for t) gives you v(t) = (-5, 9), which is 30.89 meters (if speed is expressed as m/s and time is expressed as s).

Take note that the original question lacked the units of time and velocity.

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

The rate of acceleration is

The derivative of velocity is the acceleration.

Consequently,

The acceleration rate is

The angle is located in the second quadrant.

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

To find the object's acceleration at (t=3), differentiate the velocity function twice:

[a(t) = \left(\frac{1}{2\sqrt{t-2}} - 2, 2t\right)]

Substitute (t=3) into the acceleration function:

[a(3) = \left(\frac{1}{2\sqrt{3-2}} - 2, 2(3)\right) = \left(-\frac{3}{2}, 6\right)]

So, the object's acceleration at (t=3) is ((-3/2, 6)). The rate of acceleration is (\frac{3}{2}) units per second squared, and the direction is given by the vector ((-3/2, 6)).

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.

- An object is at rest at #(8 ,2 ,9 )# and constantly accelerates at a rate of #3 m/s# as it moves to point B. If point B is at #(6 ,7 ,3 )#, how long will it take for the object to reach point B? Assume that all coordinates are in meters.
- The position of an object moving along a line is given by #p(t) = 2t - cos(( pi )/4t) #. What is the speed of the object at #t = 7 #?
- If an object is moving at #60 m/s# and accelerates to #145 m/s# over 5 seconds, what was the object's rate of acceleration?
- A cubical box consists of 4 square sides and a square base but has no top. The sides and the base are all made of thin sheet metal of uniform thickness. If the edges of the box are all 200 mm in length, how far above the base is the box’s centre of mass?
- The velocity of a sailing boat in favor of the current in a river is 18km/hr and against the current, it is 6km/hr.In which direction the boat is to be driven in order to reach the other side of the river and what will be the velocity of the boat?

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