Question

A motorist is traveling at $72kmph$ along a straight road when he observes a traffic light $200m$ ahead of him turns red. The traffic light is timed to stay red for $15sec$. If the motorist wishes to pass the light without stopping just as the signal turns green.
Determine (a) The uniform deceleration, (b) Velocity of the motorist as he passes the light.

Answer 1

(a) Let the uniform deceleration of motorcycle $=a$

Then applying second equation of motion for uniform decelaration:

$s=ut+\frac{1}{2}a{t}^2$

$\Rightarrow 20\times 15+\frac{1}{2}a\times 225=200$ $(72kmph=20m/s,s=200m,t=15s)$

$\Rightarrow a=-\frac{200}{225}m/s^2$

$\Rightarrow a=-\frac{8}{9}m/s^2$

(b) Now let velocity of motorcycle when it passes the signal $=v$

Applying first equation of motion:

$v=u+at$

$v=20-\frac{8}{9}\left(15\right)m/s$

$\Rightarrow v=-\frac{60}{9}m/s=-\frac{20}{3}m/s$