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anonymous
 5 years ago
A speeder passes a parked police car at a
constant speed of 28.4 m/s. At that instant,
the police car starts from rest with a uniform
acceleration of 2.93 m/s2.
How much time passes before the speeder
is overtaken by the police car?
Answer in units of s
anonymous
 5 years ago
A speeder passes a parked police car at a constant speed of 28.4 m/s. At that instant, the police car starts from rest with a uniform acceleration of 2.93 m/s2. How much time passes before the speeder is overtaken by the police car? Answer in units of s

This Question is Closed

JamesJ
 5 years ago
Best ResponseYou've already chosen the best response.1Let's set x = 0 where the police car is. What's the equation of motion for the two cars? \[ x_{speeder}(t) = ... what? \] \[ x_{police}(t) = ... what? \]

JamesJ
 5 years ago
Best ResponseYou've already chosen the best response.1the speeder's location xs(t) is xs(t) = 28.4t Now what's the police car's position, xp(t) ?

JamesJ
 5 years ago
Best ResponseYou've already chosen the best response.1Right, exactly. Now when are the two equal?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0set them = to each other?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0when the police car catches the speeder

JamesJ
 5 years ago
Best ResponseYou've already chosen the best response.1Set them equal and find the value of t for which that is the case.

JamesJ
 5 years ago
Best ResponseYou've already chosen the best response.1Right. t = 0 is when the driver first goes past the police car. You want the other answer.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0and it is not correct. I've already tried it previously.

JamesJ
 5 years ago
Best ResponseYou've already chosen the best response.1t = 48 sec isn't right. Check your calculation

JamesJ
 5 years ago
Best ResponseYou've already chosen the best response.1\[ 28.4 t = \frac{2.93}{2} t^2 \]

JamesJ
 5 years ago
Best ResponseYou've already chosen the best response.1\[ t = 0 \] or \[ t = \frac{2 \times 28.4}{2.93} \]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I made an error somewhere, thankyou.

JamesJ
 5 years ago
Best ResponseYou've already chosen the best response.1The position of the speeder is\[ x_s(t) = 28.4 t \]The position of the police car is \[ x_p(t) = \frac{1}{2} 2.93t^2 \] Hence the positions are equal when \[ 28.4 t = \frac{1}{2}2.93t^2 \] Now solve for t as I've written above. You can factor out a t from both sides if t is not zero, which gives you \[ \frac{1}{2}2.93t = 28.4 \] hence \[ t = \frac{2 \times 28.4}{2.93} \] Now simplify that expression.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I was making this more difficult by using quadratic equation. Thank you for the help and clarification.
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