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.

find the sum of the two horizontal vectors and the sum of the two vertical vectors

isoceles right angled triangle

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