Just as a car starts to accelerate from rest with an acceleration of 2ms^-2,a bus moving with constant speed of 10ms^-1 passes it in a parallel lane
a)how fast will the car be going when it overtakes the bus

Question

eric_d · Answer

@ganeshie8

ganeshie8 · Answer

so the bus is going at 10m/s speed, can you write the equation for its distance ?

ganeshie8 · Answer

$$\large   s =  ut + \dfrac{1}{2}at^2$$

seen this before ?

eric_d · Answer

yes

ganeshie8 · Answer

$u = 10$
$a = 0$

plugin

ganeshie8 · Answer

you get :
$$\large   s =  10t + \dfrac{1}{2}(0)t^2$$
$$\large   s =  10t ~~~~~~~~~~\color{Red}{(1)}$$

eric_d · Answer

s=10(t)+0

ganeshie8 · Answer

thats the equation for distancce travelled by the bus as time goes on

ganeshie8 · Answer

we need to find at what time the car covers this distance and overtakes the bus

ganeshie8 · Answer

lets write a distance equation for `car` also :

$u = 0$
$a = 2$

plugg them in distance equation

ganeshie8 · Answer

you get :
$$\large   s =   (0)t + \dfrac{1}{2}(2)t^2$$
$$\large   s =   t^2~~~~~~~~~\color{Red}{(2)} $$

eric_d · Answer

want to clarify this
..., a = 0 coz constant velocity

ganeshie8 · Answer

exactly !

ganeshie8 · Answer

velocity is not changing, so there is no acceleration

ganeshie8 · Answer

solve $\large \color{red}{(1)}$ and $\large \color{red}{(2)}$ for $t$

eric_d · Answer

t=10

ganeshie8 · Answer

yes ! so the car overtakes the bus exactly after 10 seconds

ganeshie8 · Answer

that means the car accelerates for 10 seconds before overtaking the bus, right ?

ganeshie8 · Answer

t = 10
u = 0

plug these in :
$\large   v = u+at$

to find the speed at which the car overtakes the bus

eric_d · Answer

v=0+a(10)

ganeshie8 · Answer

Oh yes, and you're given a = 2, 
plug that also

eric_d · Answer

v=20ms^-1

ganeshie8 · Answer

Yep ! so the car overtakes the bus exactly after 10 seconds and the speed of car when overtaking is 20 ms^-1

eric_d · Answer

Thanks @ganeshie8

ganeshie8 · Answer

np :) did u get why we have equated the equations $\large \color{red}{(1)}$ and $\large \color{red}{(2)}$ earlier  ?

eric_d · Answer

to find time..

ganeshie8 · Answer

we equated them because, the `distances travelled by both car and bus are equal` when the car overtakes the bus

eric_d · Answer

Okay, understood

ganeshie8 · Answer

good :)