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

1 Answer
May 18, 2018

Answer:

There is no impulse at that time.

Explanation:

The acceleration, #a(t)#, is the first derivative of #v(t)#.

#a(t) = (dv(t))/dt = 2cos2t -4sin4t#

Evaluating that at time #t = pi/4#,

#a(pi/4) = 2cos(pi/2) - 4sinpi = 2*0 - 4*0 = 0#

Since the acceleration is zero, the force applied to this object is zero.

Now impulse. Impulse is #"force"*"time"#, where time is the length of time that the force was applied. The question does not refer to a time duration, just the moment when #t = pi/4#.

So "impulse" would not really apply to this situation even if the force had not calculated out to be zero.

I hope this helps,
Steve