Question

21. For the one-dimensional motion of a particle.
described by position x = t + cost (where t is time in
s and x is in m), the velocity of particle is zero at time
t equals to
(1) 0.3 s
(2) 1 s
(3) 0.25
(4) 1.57 s

Answer 1

d because dx/dt where zero velocity zero

Answer 2

Answer:

(4) 1.57 s

Explanation:

Given that

X = t + cos t

Velocity of particle given as

$V=\dfrac{dX}{dt}$

X = t + cos t

Now by differentiating X with respect to time t,we get

$\dfrac{dX}{dt}=1-sin t$

$V=\dfrac{dX}{dt}$

So

V=1-sin t

V=1-sin t = 0   (given that V=0)

1 = sin t

$t=sin^{-1}1$

t= 90 °=π/ 2

As we know that

π = 3.14

t= π/2 = 3.14/ 2  = 1.57 s

At t= 1.57 s,V= 0 m/s

(4) 1.57 s