Question

A particle starts from its origin and components of its velocity parallel to the axis of coordinates at time t are 2t+3 and 4t. Find its path

Answer 1

Answer:

Since acceleration is in y-direction and is constant, let's take a

y

=α

Thus

dt

dv

y

=α

Integrate to get, v

y

=αt+k.

Since the particle starts moving at t=0, thus k=0.

Thus, v

y

=αt

Also, integrate once again to get, y=

2

αt

2

(y=0 at t=0)

Now, y=βx

2

and hence x=

β

y

=

2β

αt

2

Differentiate with time to get, v

y

=β(2x)(v

x

)

Solve to get v

x

=

2β

2β

αt

2

αt

Solving above gives, v

x

=

2β

α

Step-by-step explanation:

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