Question

Q3: Force applied on a body is given by F = (3t2 - 2t + 10) N where t is in sec..
Find impulse in t = 0 to t = 2 sec (in kg m/sec)

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