Question

The velocity of a particle moving back and forth on a line is vequalsStartFraction ds Over dt EndFraction equals6 sine (2 t )StartFraction m Over sec EndFraction for all t. If sequals0 when tequals​0, find the value of s when tequalsStartFraction pi Over 2 EndFraction sec.

Answer 1

Answer:

s = 6 m

Step-by-step explanation:

The value of the velocity v is given as:

$v = \frac{ds}{dt} = 6 sin(2t)$ m/s

To find s, we have to integrate and apply the initial values of s = o when t = 0:

$\frac{ds}{dt} = 6 sin(2t)\\\\\int\limits^s_0 {ds} = \int\limits^t_0 {6sin(2t)} \, dt\\\\s|^s_o = -3cos(2t)|^t_o\\\\s - 0 = -3cos(2t) -(-3cos(0))\\\\s = -3cos(2t) + 3(1)\\\\s = -3cos(2t) + 3$

When t = π/2, s will be:

s = -3cos(2 * π/2) + 3

s = -3cos(π) + 3

s = -3(-1) + 3

s = 3 + 3

s = 6 m