Answer to Question #164894 in Mechanics | Relativity for Faith Horton

Question

b.A taxi reaches a police officer while travelling at 30 m/s on the highway. The officer immediately signals the taxi which decelerates uniformly and comes to a complete stop in 5s. Assume zero reaction time.

i.Draw a velocity-time graph to represent the motion of the taxi from the moment the officer

signals to when the taxi comes to a stop. (2)

ii.Determine the distance travelled by the taxi from the time the police signals until the taxi stops. (3)

iii.If the speed limit is 80 km/h, determine whether or not the driver should receive a speeding

Answer 1

(i)

ii) We have given,

Initial Velocity ,$u= 30m/s$

time, $t=5s$

Now, using first equation of motion

$v= u+ a\times t$

where, v=final velocity

a=acceleration

Now,

$0=30+a(5)\\\Rightarrow a=-6m/s^2$

Using second equation of motion

$s=ut+\dfrac{1}{2}(at^2)$

$s=30(5)+\dfrac{1}{2}(-6)(5)^2$

$s=150-75\\ s=75m$

iii) If the speed limit is $30km/h=30\times \dfrac{5}{18}$

$=22.22\text{ms}^{-2}$

Hence, the driver should receive over speeding fine.