"A body moves in a straight line such that, t s after passing through a fixed point O, its displacement from O is s m. The velocity v ms^-1 of the body is such that v = 5cos(4t)"
a) Write down the velocity of the body as it passes through O.
b) Find the value of t when the acceleration of the body is first equal to 10ms^-2 .
For a) I got v = 5ms^1 .
For b) I did the following:
dv/dt = -20sin(4t)
10 = -20sin(4t)
-0.5 = sin(4t)
How do I get rid of the sine? Do I use the arcsine? When I do that I get 4t = (-1/6)pi , and after I divide it by 4 I get (-1/24)pi, which is not the correct answer... Any help would be appreciated!
Since time got no directions(at least in kinematics), don't take $-pi/6$ as the value. Since it is mentioned that the first time the acceleration goes to $10 ms^-2$. The value will be $4t= 210$. So the answer will be $52.5 sec$