A bullet is fired from a gun. The force on the bullet is given by F = 600 − 2 × 10 5 t , where F is in newton and t is in seconds. If the force on the bullet becomes zero as soon as it leaves the barrel, then the average impulse imparted to the bullet is

Step-by-step solution

Given F = 600 − ( 2 × 10 5 t ) The force is zero at time, t , given by 0 = 600 − 2 × 10 5 t ⇒ t = 600 2 × 10 5 = 3 × 10 − 3   seconds ∴     Impulse = ∫ 0 t F d t = ∫ 0 3 × 10 − 3 ( 600 − 2 × 10 5 t )   d t = [ 600 t − 2 × 10 5 t 2 2 ] 0 3 × 10 − 3 = 600 × 3 × 10 − 3 − 10 5 ( 3 × 10 − 3 ) 2 = 1 . 8   –   0 . 9   =   0 . 9   N