The velocity of a particle moving in straight line depends on its position as v= 3sin [(pi /2) + x - Physics - Motion In A Plane

Question

The velocity of a particle moving in straight line depends on
its position as v= 3sin [(pi /2) + x ] m/s Find the acceleration of
the particle when at x = pi / 4 (Ans : -9/2 m/s)

Somnath physics · Accepted Answer

Given,
v =
3 sin(Ï€/2
+x)
=> v =
3 cos(x)
=> a =
dv/dt = -3 sin(x) dx/dt
=> a =
-3v sin(x)
=> a =
-3[3 cos(x)] sin(x)
=> a =
-(9/2) sin(2x)
Thus,
[a]Ï€/4=
-(9/2) sin(Ï€/2) = -(9/2)
m/s2

The velocity of a particle moving in straight line depends on its position as v= 3sin [(pi /2) + x ] m/s. Find the acceleration of the particle when at x = pi / 4. (Ans : -9/2 m/s)