A particle moves along the x-axis such that its position is given by x ( t ) = 3 t 2 − 12 t + 5 , where x is in meters and t is in seconds. What is the magnitude of the particle's velocity (in m/

Question

A particle moves along the x-axis such that its position is given by x ( t ) = 3 t 2 − 12 t + 5 , where x is in meters and t is in seconds. What is the magnitude of the particle's velocity (in m/s) at t = 3 s ?

TestHub · Accepted Answer

The velocity of the particle is the derivative of its position with respect to time: v ( t ) = d t d x ​ = d t d ​ ( 3 t 2 − 12 t + 5 ) v ( t ) = 6 t − 12 To find the velocity at t = 3 s , substitute t = 3 into the velocity equation: v ( 3 ) = 6 ( 3 ) − 12 = 18 − 12 = 6 m/s

Physics - Kinematics Question with Solution | TestHub

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