At that instant a motor bike starts from rest in a given direction, a car overtakes the motor bike, both moving in the same direction.The speed time graphs for motor bike and car are represented by `OAB` and `CD` respectively.Then

Options

A. at `t=18s` the motor bike and car are `180m` apart.
B. at `t=18s` the motor bike and car are `720m` apart.
C. the relative distance between motor bike and car reduce to zero at `t=27 s` and both are `1080 m` far from origin
D. the relative distance between motor bike and car always remains same.

Answer

A, C

Explanation

Distance travelled by motor bike at `t=18 s`
`S_("bike")=S_(1)=1/2(18)(60)=540m`
Distance travelled by car at `t=18s`
`S_("car")=S_(2)=1/2(18)(40)=720m`
Therefore, seperation between them at `t=18s` is `180m`. Let seperation between them decreases to zero at time `t` beyond `18s`.
Hence, `S_("bike")=540+60t` and `S_("car")=720+40t`
`S_("car")-S_("bike")=0 rArr 720+40t=540+60t`
`t=(18+9)s=27s` from start and distance travelled by both is `S_("bike")=s_("car")=1080m`