# The distince $x$ meters traveled by a vehical in time $t$ seconds after the brakes are applied is given by:$\;x=20 t-\large\frac{5}{3}$$t^{2}. Determine the speed of the vehicle (in km/hr) at the instant the brakes are applied This is part 1st of a 2 part question, split as 2 separate questions here. ## 1 Answer Toolbox: • If s=f(t) is the distance function, representing the distance 's' travelled by a particle in time t, then the velocity and acceleration functions are v=\large\frac{ds}{dt}$$=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 $20\;m/sec$