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Question :
The displacement x of a particle along a straight line at time t is given by
- x = a。+ a₁t + a₂t² ;
calculate the acceleration of the particle
Answer :
Given that, x = a。+ a₁t + a₂t²
★ Velocity of particle :
We know that differentiation of displacement wrt time gives velocity
- v = dx/dt
➠ v = d(x = a。+ a₁t + a₂t²)/dt
➠ v = 0 + a₁ + 2a₂t
➠ v = a₁ + 2a₂t
★ Acceleration of particle :
We know that differentiation of velocity wrt time gives acceleration.
- a = dv/dt = d²x/dt²
➠ a = d(a₁ + 2a₂t)/dt
➠ a = d(a₁)/dt + d(2a₂t)/dt
➠ a = 0 + 2a₂
➠ a = 2a₂ m/s²
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