# What is the instantaneous velocity of an object moving in accordance to # f(t)= (e^(t^2),2t-te^t) # at # t=-1 #?

To find the instantaleous velocity we have to find the derivative of the previous law.

and so:

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

To find the instantaneous velocity of an object moving according to the function ( f(t) = (e^{t^2}, 2t - te^t) ) at ( t = -1 ), we need to differentiate the function with respect to time ( t ) to get the velocity vector, and then evaluate it at ( t = -1 ).

The velocity vector ( v(t) ) is given by the derivative of the function ( f(t) ) with respect to ( t ):

[ v(t) = \frac{d}{dt} (e^{t^2}, 2t - te^t) ]

Differentiating each component separately, we get:

[ v(t) = (\frac{d}{dt} e^{t^2}, \frac{d}{dt} (2t - te^t)) ]

[ v(t) = (2te^{t^2}, 2 - (t + 1)e^t) ]

Now, we can evaluate ( v(t) ) at ( t = -1 ):

[ v(-1) = (2(-1)e^{(-1)^2}, 2 - ((-1) + 1)e^{-1}) ]

[ v(-1) = (-2e^{-1}, 2 - (0)e^{-1}) ]

[ v(-1) = (-2e^{-1}, 2) ]

So, the instantaneous velocity of the object at ( t = -1 ) is ( (-2e^{-1}, 2) ).

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

- How do you find f'(x) using the definition of a derivative # f(x) = x^2 + x#?
- Using the limit definition, how do you find the derivative of #f(x) = 3x^2 + 8x + 4 #?
- How do you use the definition of a derivative to find the derivative of #G(t) = (1-6t)/(5+t)#?
- What is the average value for #f(x)=8x-3+5e^(x-2)# over the interval [0,2]?
- What is the equation of the line tangent to #f(x)= 3x^2 - 12x-5 # at #x=-1#?

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