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.

Q. The motion of a particle is described by the equation x = at +

b t^{2}

, where a = 15 cm

s^{- 1}

and b = 3 cm

s^{- 2}

. Its instantanous velocity at t = 3 s will be

Q. The distance travelled by a particle in time

t

is given by

s = (2.5 m / s^{2}) t^{2}

. Find
(a) the average speed of the particle during the time

0

5.0 s

, and
(b) the instantaneous speed at

t = 5.0 s .

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A particle's motion is given by s=a(t+b(e(−tb)−1)), where (s is in metre, a and b are constants and t is in sec). What will be the instantaneous speed of the particle at t=∞

The correct option is A aAs we know that instantneous speed =dsdt=d(a(t+b(e−tb−1)))dt⇒v=adtdt+abd(e−tb−1)dt⇒v=a(1−e−tb) Putting the value of t=∞, in the equation we get v=a

A particle's motion is given by $s = a (t + b (e^{(- \frac{t}{b})} - 1))$ , where ( $s$ is in metre, $a$ and $b$ are constants and $t$ is in sec). What will be the instantaneous speed of the particle at $t = \infty$