Calculating the time of collision of two vehicles.

Question

I have the following problem but I'm not sure how to get started. I have a car that is $14m$ behind a lorry. The car's initial velocity is $20 ms^{-1}$ and it is decelerating at $7.6 ms^{-2}$, whilst the lorry's initial velocity is $5.0ms^{-1}$ and it is decelerating at $1.1ms^{-2}$. I need to calculate at what time the collision would occur if $t=0s$ is the time at which both drivers apply the brakes. I understand I probably need to use SUVAT equations to solve this problem. I also know that a collision would only occur if the distance travelled by the car is more than or equal to the distance travelled by the lorry plus the initial separation distance. However, I don't really know how to proceed.

Answer 1

Hint…using $s=ut+\frac12 a t^2$, write down the displacement of each vehicle at time $t$.

Subtract the displacement of the lorry from that of the car and set this equal to $14$. Solve for $t$.

I hope this helps.