Calculating Time for Bus to Catch Anna - Motion Problem

[TyErd]

A cyclist, Anna is traveling at a constant speed of 12m/s when she passes a stationary bus. The bus starts moving just as Anna passes, and it accelerates uniformaly at 1.5m/s.

How long does the bus take to catch Anna??

 

[rl.bhat]

Write down the relevant equations. Show your attempts.

 

[TyErd]

alright this is what i did but i didnt get the correct answer.

equation formed
12t=0.5*8*12 + 1.5t(t-8)

simplify it down and i got 1.5t^2-12t-48=0, t>0 is 10.9

answer is suppose to be 16

 

[rl.bhat]

Bus starts from rest. So in time t the distance moved by the bus is 1/2*a*t^2. During that time distance moved by the cyclist is v*t. If the meet after this time, these distances must be equal.

 

[TyErd]

is a the acceleration? and why is it t^2?

if you can, can you show me your full working out

 

[rl.bhat]

Yes. a is the acceleration. What is the kinematic equation which contains initial velocity, acceleration, time and displacement? And unit of acceleration is m/s^2

 

[TyErd]

ohhhhhhhhhhhhhhh...thnx i get it now. I am suppose to use x=ut+1/at^2 formula

 

[rl.bhat]

Yes.