Question

The displacement of an object at any instant is given by x = 30+ 20T2 where x in m
and t is in s. The acceleration of the object will be
(a)30m/s2
(b) 40m/s2 fe) 50m/s?
(d) zero

Answer 1

So we are given displacement...

S = 30 + 20 T^2

Differentiating with respect to time

...v = dx/dt

v = 40T

Differentiating again with respect to time...

a = dv/dt

a = 40 m/s^2

Answer 2

ACCELERATION IS 40 m/s² (Option b)

Given:

• x = 30 + 20t²

To find:

• Acceleration of object

Calculation:

Acceleration of a particle can be calculated by second order derivative of the displacement function with respect to time

$x = 30 + 20 {t}^{2}$

$\implies \: v = \dfrac{dx}{dt}$

$\implies \: v = \dfrac{d(30 + 20 {t}^{2}) }{dt}$

$\implies \: v = 40t$

Now, acceleration will be :

$a = \dfrac{dv}{dt}$

$\implies a = \dfrac{d(40t)}{dt}$

$\implies a = 40 \: m {s}^{ - 2}$

So, acceleration is 40 m/s².