1d kinematics dog,cat

Question

A dog is running toward a cat that is 1.5 m away. Initially at rest, the cat sees the dog running toward her and accelerates away from the dog at 0.85 m/s/s directly toward a small pet door that is another 1.5 m in front of the cat (too small for the dog, but OK for the cat to fit through). Seeing the small window ahead, the dog (initially moving at 1.7 m/s) begins to slow down at 0.3 m/s/s. We need to figure out if the cat makes it out of the door before the dog arrives, and so how far does the dog go by the time the cat reaches the door? Report your answer to the tenths decimal place.

Answer 1

You need to generate equations for the position of the cat and the dog with the same time and position variables. Let's make the dog s position at t = 0 as 0 (x₀) and the dog's velocity as 1.7 m/s (v₀ ) . The cat has an x₀ = 1.5 m and v₀ = 0.

the cat's equation of motion is x = x₀ + (1/2)a_ct²

the dog's equation of motion is x = x₀ + v₀t - (1/2)a_dt²

where ac is the cat's acceleration and ad is the deceleration of the dog (I could have put it in as the acceleration, but then you would have to remember to make the sign negative. )

Use the cat equation to solve for time, given x = 3m

Use the dog equation to solve for the position the dog is in at that time.

Hope that helps!