If the particle's velocity is governed by: v = 2s +1 where s is in [ft] and v is in [ft/s], find the particle's acceleration at s = 3 ft. find how long it takes the particle to reach 100 ft if its initial position was 0 ft.

The particle takes 3.41 sec to reach 100 ft.

Explanation:

Given that,

Velocity v= 2s+1

Distance s = 100 ft

Acceleration :

The acceleration is the first derivative of the velocity of the particle.

But,

Multiply by 2 in both side

On integrating both side

On differentiating w.r.to t

The acceleration at s = 3

(II). We need to calculate the time

Using equation of motion

....(II)

We need to calculate the initial velocity

The particle's velocity is

v= 2s+1

Put the value of s in the equation

Now, Put the value in the equation (II)

t can not be negative.

Hence, The particle takes 3.41 sec to reach 100 ft.

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