# An object's two dimensional velocity is given by #v(t) = ( e^t-2t , 2t-4e^2 )#. What is the object's rate and direction of acceleration at #t=a #?

The rate of acceleration is

The derivative of the velocity is the acceleration.

Consequently,

The acceleration rate is

The path is

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

The object's acceleration at ( t = a ) is ( a(t) = (1 - 2, 2) ) or ( a(t) = (-1, 2) ), depending on the value of ( a ). The rate of acceleration is (\sqrt{(-1)^2 + 2^2} = \sqrt{5}). The direction of acceleration is given by the unit vector ( \frac{a(t)}{|a(t)|} = \left(\frac{-1}{\sqrt{5}}, \frac{2}{\sqrt{5}}\right) ).

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 an object begins at the origin, will its displacement from the origin be the same as its position?
- A red car and a green car move toward each other in adjacent lanes and parallel to an x axis. At time t = 0, the red car is at xr = 0 and the green car is at xg = 216 m. If the red car has a constant velocity of 27.0 km/h ?
- If a projectile is shot at an angle of #(5pi)/12# and at a velocity of #1 m/s#, when will it reach its maximum height?
- A particle moves along a straight line such that its displacement any time t is given by: s=( #t^3 - 3t^2 +2#)m. The displacement when the acceleration becomes zero is?
- A boat is trying to cross a river that is flowing at 2 m/s. The boat can travel at 4m/s. What is the resultant 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