Question

The engine of a motorcycle can produce a maximum acceleration of $5m{s}^{-2}$. Its brakes can produce a maximum retardation of $10m{s}^{-2}$. What is the minimum time in which the motorcycle can cover a distance of $1.5km$?

Answer 1

let’s say that the bike starts from zero and accelerates at 5m/s^2 for t secs until it reaches v m/s

Then $(v-0)/t=5$ or $v=5t$, and $-v=-5t$

If T is the total time then there is T-t secs left to stop using a deceleration of

$-10m/s^2,$so

$(0-v)/(T-t)=-10$

$-v=-10T+10t$ but$-v=-5t$, so

$-5t=-10T+10t$

$10T=15t$

$T=3t/2$

Now use the piece of information given the distance 1500m

$\left[1/2\right]vT=1500$

$vT=3000$ . Note we have v and T in term of one [1] unknown t

$\left[5t\right]\left[3t/2\right]=3000$

$15t^2=6000$

$t^2=400$

$4t=20$

So$T=3t/2=3\left[20\right]/2=30secs$