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a-t Graph

The motion of...

Question

The motion of a particle is described by the equation X = at + bt² , where a= 15cm s^-1 and b =3cm s^-2. Its instantaneous velocity at t= 3 s will be ______ CM s^-1.

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Solution

X = at + bt^2

Plug in the values of a and b.

x = 15t + 3t^2

We know that x/t gives v

So differentiating the equation w.r.t t,
dx/dt = 15 + 2 x 3t

v = 15 + 6t

Now it's given that t = 3

So the instantaneous velocity will be 15 + 6 x 3 = 33 cm/s

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