At time t second, a particle of mass 3 kg has position vector r → metre where r → = (3 t) i ^ - (4 cos t) j ^ . The impulse of the force during the time interval 0 ≤ t ≤ π 2 is

Question

At time t second, a particle of mass 3 kg has position vector r → metre where r → = (3 t) i ^ - (4 cos t) j ^ . The impulse of the force during the time interval 0 ≤ t ≤ π 2 is, 12 j ^ N-s, 9 j ^ N-s, 4 j ^ N-s, 14 j ^ N-s

MARKS App · Accepted Answer

∵ r → = 3 t i ^ - 4 cos ⁡ t j ^ ∴ v → = d r → d t = 3 i ^ + 4 sin ⁡ t j ^ ∴ a → = d 2 r → d t 2 = 4 cos ⁡ t j ^ ∴ F → = m a → = 12 cos ⁡ t j ^ ∴ Impluse = ∫ 0 π 2 F d t = 12 ∫ 0 π 2 cos ⁡ t d t = 12 sin ⁡ t 0 π 2 = 12 N - s The direction of impulse will be in the direction of force. ∴ Impulse = 12 N - s j ^

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