Question

f=3t^2+5t. find impulse t=0 to t=2sec.​

Answer 1

Answer:

We have been provided equation of force.

F = (3t² - 2t + 10) N

We have to find impulse in t = 0s to t = 2s

➠ As per Newton's second law of motion, Force is defined as the rate of change of linear momentum.

F = dp / dt

⇒ dp/dt = F = 3t² - 2t + 10

⇒ dp = (3t² - 2t + 10) dt

Integrating on both sides, we get

⇒ p = 3t³/3 - 2t²/2 + 10t

⇒ p = t³ - t² + 10t

Putting limits (0 to 2), we get

⇒ p = (2³ - 0³) - (2² - 0²) + 10(2 - 0)

⇒ p = 8 - 4 + 20

⇒ p = 4 + 20

⇒ p = 24 kg m/s