Question

A particle moves according to the equation x = 3+4t+6t²+4t³. Find its velocity and acceleration at all times. When does its velocity equal 10 m/s? What is its acceleration at that instant?

Answer 1

• dx/dt = v = 4 + 12t + 12t^2

• dv/dt = a = 12 + 24t

• v = 4 + 12t + 12t^2 = 10

=> 12t + 12t^2 = 6

=> t + t^2 = 1/2

=> t^2 + t - 12 = 0

=> t = 3 sec

• a = 12 + 14t

=> at t = 0

=> a = 12 m/s^2

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