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- If $s=f(t)$ is the distance function, representing the distance 's' travelled by a particle in time t, then the velocity and acceleration functions are $v=\large\frac{ds}{dt}$$=t'(t)$ and $a=\large\frac{d^2s}{dt^2}=f''(t)$
- When a particle starts from rest,velocity v and time t are 0. When a particle is thrown up, it reaches maximum height at which $v=0$ and then falls back to earth. When a moving particle comes rest, $v=0$

$x=20t-\large\frac{5}{3}$$t^2$ when the brakes are applied

Velocity is $\large\frac{dx}{dt}$$=20- \large\frac{5}{3}$$ \times 2t$

$\qquad\qquad=20-\large\frac{10}{3}$$t$

$t=0$ When the brakes are applied.

The speed at $t=0$ is $20\;m/sec$

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