Question

origin. Find its velocity when its displacement is 4 m
010. A particle starts with acceleration a - 2s, where's' is its displacement as measured from a fixed​

Answer 1

Answer:

Let’s begin with a particle with an acceleration a(t) is a known function of time. Since the time derivative of the velocity function is acceleration,

d

d

t

v

(

t

)

=

a

(

t

)

,

we can take the indefinite integral of both sides, finding

∫

d

d

t

v

(

t

)

d

t

=

∫

a

(

t

)

d

t

+

C

1

,

where C1 is a constant of integration. Since

∫

d

d

t

v

(

t

)

d

t

=

v

(

t

)

, the velocity is given by

v

(

t

)

=

∫

a

(

t

)

d

t

+

C

1

.

Similarly, the time derivative of the position function is the velocity function,