The displacement of a particle is represented by the following equation : x = 3t3 + 7t2 + 5t + 8 where x is in metre and t in second. The acceleration of the particle at t = 1 is :-
Question
The displacement of a particle is represented by the following equation : x = 3t3 + 7t2 + 5t + 8 where x is in metre and t in second. The acceleration of the particle at t = 1 is :-
Solution
To find the acceleration of the particle at a given time, we first need to find the velocity and then the acceleration. The velocity is the first derivative of the displacement function, and the acceleration is the first derivative of the velocity function.
The given displacement function is x = 3t^3 + 7t^2 + 5t + 8.
Step 1: Find the velocity function by taking the first derivative of the displacement function. v = dx/dt = d/dt(3t^3 + 7t^2 + 5t + 8) = 9t^2 + 14t + 5.
Step 2: Find the acceleration function by taking the first derivative of the velocity function. a = dv/dt = d/dt(9t^2 + 14t + 5) = 18t + 14.
Step 3: Substitute t = 1 into the acceleration function to find the acceleration at t = 1. a(1) = 18(1) + 14 = 18 + 14 = 32 m/s^2.
So, the acceleration of the particle at t = 1 is 32 m/s^2.
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