The velocity of an object with a mass of #2 kg# is given by #v(t)= t^3 + 3 t^2 #. What is the impulse applied to the object at #t= 4 #?

Answer 1

#I (4) =2 (4*4^2 +3*4^2) = 7*4^2 = 112 N s#
Careful however Impulse is not #mv(t)# evaluate at #t = 4 s#
it is Force applied for a finite amount of time #F*Deltat#
in the limit #I = int_(t_1)^(t_(2))Fdt #

This is a straight implementation of the impulse equation i.e. #F = m(dv)/dt # Newton law ==> (1) #I = F dt = m(dv) # Impulse equation ==> (2) While the question is not clear I will make the assumption the Force was applied for 4 seconds causing the change in speed from #v(0) = 0 -> v(4)# and #I (4) =2 (4*4^2 +3*4^2) = 7*4^2 = 112 N s#
Sign up to view the whole answer

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

Sign up with email
Answer 2

To find the impulse applied to the object at ( t = 4 ), you need to calculate the change in momentum. Impulse is defined as the change in momentum, which can be found by integrating the force over the time interval. In this case, impulse ( J ) can be calculated using the formula:

[ J = \int_{t_1}^{t_2} F(t) , dt ]

Given that velocity ( v(t) = t^3 + 3t^2 ), the force ( F(t) ) can be found by taking the derivative of velocity with respect to time, ( F(t) = \frac{dv}{dt} ). Then, calculate the impulse ( J ) by integrating the force from ( t = 0 ) to ( t = 4 ):

[ J = \int_{0}^{4} F(t) , dt ]

After integrating, you'll have the impulse applied to the object at ( t = 4 ).

Sign up to view the whole answer

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

Sign up with email
Answer from HIX Tutor

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.

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.

Not the question you need?

Drag image here or click to upload

Or press Ctrl + V to paste
Answer Background
HIX Tutor
Solve ANY homework problem with a smart AI
  • 98% accuracy study help
  • Covers math, physics, chemistry, biology, and more
  • Step-by-step, in-depth guides
  • Readily available 24/7