You want to visit your friend over term break. To save money, you decide to travel there by train. You are late and run as fast as you can, but just as you reach one end of the platform your train departs, 30 m ahead of you down the platform. You are running at your fastest speed of 8 m/s and the train is accelerating at 1 m/s2. You can run along the platform for 50 m before you reach a barrier. Will you catch your train?
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Let's measure distance from where you are right at the moment described.
Your position at time t is
p(t) = 8t
The train's position called it q(t) is another function? What is it? You know that
q(0) = 30.
The question is
- for what t is p(t) = q(t); call it t'
- and is p(t') < 1000 for that particular value of time t'?
If so, then you can catch the train in time. If not, no.
btw, it's not great to "drop and run". Better to hang around for at least a while after answering your question to see if there is someone there to engage with you on it.