A particle starts moving from origin with velocity u = 2 i ^ + 4 j ^ under an acceleration of a = 4 t i ^ − 6 k ^ where t is the time elapsed since it started from origin. Find the value of t at which acceleration is perpendicular to initial velocity.

When u and a are perpendicular u ⋅ a = 0 ( 2 i ^ + 4 j ^ ) ( 4 t i ^ − 6 k ^ ) = 0 8 t = 0 t = 0

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Physics - Kinematics Question with Solution | TestHub

PhysicsKinematics2-D & 3DEasy2 minQB

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A particle starts moving from origin with velocity $u = 2 \hat{i} + 4 \hat{j}$ under an acceleration of $a = 4 t \hat{i} - 6 \hat{k}$ where $t$ is the time elapsed since it started from origin. Find the value of $t$ at which acceleration is perpendicular to initial velocity.

Answer:

Solution:

When $u$ and $a$ are perpendicular $u \cdot a = 0$

$(2 \hat{i} + 4 \hat{j}) (4 t \hat{i} - 6 \hat{k}) = 0$

$8 t = 0$ $t = 0$

Stream:JEESubject:PhysicsTopic:KinematicsSubtopic:2-D & 3D

⏱ 2mℹ️ Source: QB

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