Question

If v = (5s) m>s, where s is in meters, determine a at s = 1 m.​

Answer 1

The acceleration at s=1m is 25m/s^2

Given that,

Velocity v= 5s m/s

To find acceleration a at s=1m

Acceleration: The rate of change of velocity of an object is called acceleration.It is a vector quantity.

Velocity: is the rate of change of position of an object with time in a given direction.

Formula of velocity = displacement / time.

We know that acceleration is the derivative of velocity with respect to time.

We also know that, time derivative of displacement is known as velocity.

$a=\frac{dv}{dt} \\a=\frac{d}{dt}(5s)\\a=\frac{d}{ds}(5s)*\frac{ds}{dt} \\a=5*\frac{ds}{dt}\\a=5v\\a=5vm/s^{2}$

When s=1,

And, v=5s m/s

So, =5*1m/s

      =5m/s

Therefore acceleration a at 1m = 5v = 5*5=25m/s^2

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