The velocity of a particle varies with time as v = − t i ^ − e − t j ^ + t c k ^ . If the particle accelerates perpendicular to the direction of its motion after one second. The value of c is :

Question

The velocity of a particle varies with time as v = − t i ^ − e − t j ^ ​ + t c ​ k ^ . If the particle accelerates perpendicular to the direction of its motion after one second. The value of c is :

TestHub · Accepted Answer

v = − t i ^ − e − t j ^ ​ + t c ​ k ^ a = dt d v ​ = − i ^ + e − t j ^ ​ − t 2 c ​ k ^ At t = 1 sec a ⊥ V ⇒ a ⋅ v = 0 = + t − ( e − t ) 2 − t 3 c 2 ​ = 1 − e − 2 × 1 − c 2 = 0 c = 1 − e − 2 ​ = 1 − e 2 1 ​ ​

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