First slide

Instantaneous acceleration

Question

A particle moves along with X-axis. The position x of particle with respect to time t from origin is given by $x = b_{0} + b_{1} t + b_{2} t^{2}$ . The acceleration of particle is

Moderate

A

$b_{0}$
B

$b_{1}$
C

$b_{2}$
D

$2 b_{2}$

Solution

Distance, $x = b_{0} + b_{1} t + b_{2} t^{2}$
Velocity, $v = (\frac{d x}{d t}) = b_{1} + 2 b_{2} t$
Acceleration, $a = \frac{d^{2} x}{d t^{2}} = 2 b_{2}$

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