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Head-on Collision: Kinematics

APPH12-OYXNIS

Ronnie Racer and Daring Debbie are about to play chicken on a $100\ \text{m}$ deserted stretch of road. Ronnie lines up his car at one end facing East. Debbie lines up her car at the other end facing West. They will both start their cars at the same time. The good news is that the cars can drive themselves, so nobody will get hurt when the cars collide.

Ronnie's car's speed, in $\text{m/s}$, is described by the function $v(t)=6.0t$, where $t$ is measured in seconds.

Debbie's car's speed, in $\text{m/s}$, is described by the function $v(t)=2.0t$, where $t$ is measured in seconds.

Assuming neither car reaches its maximum speed, when will the two cars collide?

A

$t=4.0\ \text{s}$

B

$t=5.0\ \text{s}$

C

$t=8.0\ \text{s}$

D

$t=12.5\ \text{s}$