Displacement x versus $t^2$ graph is shown for a particle. The acceleration of the particle is :
- $2\,m/s^2$
- $4\,m/s^2$
- $8\,m/s^2$
- zero
The Correct Option is B
Solution and Explanation
x = Slope $\left(t^{2}\right) $
$x =\frac{2-0}{1-0}\left(t^{2}\right) $
$x =2 t^{2} $
$\frac{d x}{d t} =4 t $
$\frac{d^{2} x}{d t^{2}} =4$
$a =4 \,m / s ^{2}$
$[\because \frac{d^{2} X}{d t^{2}}=a]$
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Concepts Used:
Acceleration
In the real world, everything is always in motion. Objects move at a variable or a constant speed. When someone steps on the accelerator or applies brakes on a car, the speed of the car increases or decreases and the direction of the car changes. In physics, these changes in velocity or directional magnitude of a moving object are represented by acceleration.
