Question

Displacement of a particle is given by the expression x = 3t2 + 7t – 9, where x is in meter and t is in seconds. What is acceleration?

CLASS - XI PHYSICS (Kinematics)

Answer 1

acceleration = $\frac{ d^{2} x}{d t^{2} }$

x = 3t² + 7t - 9

$\frac{dx}{dt}= \frac{d}{dt}(3 t^{2} +7t-9)=6t+7$

$\frac{ d^{2} x}{d t^{2} }$ = $\frac{d}{dt}( \frac{dx}{dt} ) = \frac{d}{dt}(6t-7) = 6$

Thus acceleration is 6m/s²

Answer 2

x = 3t² + 7t - 9
differentiate displacement w.r.t. t to get velocity
after differentiating
 dx/dt = 6t + 7                           { differentiation of $x^{n}=nx^{n-1}$}
v = 6t + 7
again differentiating velocity w.r.t. t to get acceleration
dv/dt = 6 
a = 6 m/s²