A particle is moving with the given data.

Question

1) a(t) = 3 cos t - 2 sin t, s(0) = 0, v(0)= 4 

2)a(t) = t^2 - 4t + 6, s(0)=0, s(1)=20

Answer 1

1.

Acceleration a(t) = 3cost-2sint

Disatnce at initial position s(0) = 0

Velocity at intial position  v(0) = 4

From the formula , 

                         

The velocity at initial position ,V(0) = 4

Now substituting the values

So, the velocity  .

Now,calculating the distance:

From the relation 

Distance at initial position S(0) =0

Hence the distance ,.

Answer 2

2.

Acceleration 

From the relation 

.

Distance 

.

.

Distance at t=0 ,S(0) =0

Now substituting the values

 

Distance at t = 1sec,

 

So , 

Hence the distance is .