Question

if x denotes displacement in time t and x=a cost, then acceleration is
(1) a cost
(2) -a cost t
(3) a sin t
(4) -a sin t​

Answer 1

Answer:

2) -acost

double differentiate it

Answer 2

Explanation:

The displacement of the object at time t is given by :

$x=a\ cost$

We know that velocity is given by :

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

$v=\dfrac{d(a\ cost)}{dt}$

$v=-a\ sint$

We know that acceleration is given by:

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

$a=\dfrac{d(-a\ sint)}{dt}$

$a=-a\ cost$

So, the acceleration of the object is $-a\ cost$. Hence, this is the required solution.