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54321S · May 19, 2013, 06:49 AM

A van passes a junction violating traffic regulation at 20ms-1. A cop who is at the junction quickly starts his bike and chases the van. He spends 10 seconds to start his bike and accelerate at 3ms-2. The max speed of the bike is 30ms-1.
(1) Find whether the cop reaches the van during his acceleration or during his max speed.
(2) Find the distance between the junction and the point of meeting the cop to the van.

I just started the mechanics lesson in our class and this problem is kind of difficult.

ebaines · May 20, 2013, 06:49 AM

You need to set up two equations for the motion of tehe van and the bike, and see at what time the two intersect. The motion of the van is simply speed times time:

$<br /> x_{van} = v_{van} t = 20 \frac m s t$

The motion of the bike is delayed 10 seconds, then accelerate at a constant rate:

$<br /> x_{bike} = \frac 1 2 a (t-10)^2 = \frac 1 2 (3 \frac m {s^2}) (t-10)^2<br />$

Set these equal and solve for t. Then find the bike's speed at that value of time - if it's greater than 30 m/s then the bike must have actually hit it's top speed before catching the van.