Basic Kinematics problem, why my method is invalid

AI Thread Summary
The discussion revolves around a kinematics problem where a motorist travels at a constant speed while a police officer accelerates to catch up. The initial attempt incorrectly assumes that distance can be calculated using the equation d = vt, which only applies to constant velocity scenarios. The correct approach involves using the full kinematic equation d(t) = d_o + v_o t + 1/2 a t^2 to account for the officer's acceleration. The mistake was clarified, emphasizing the necessity of using appropriate equations when acceleration is present. Understanding these principles is crucial for solving kinematics problems accurately.
Yousufshad
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Homework Statement


A motorist drives along a straight road at a constant speed of 14.4m/s. Just as she passes a parked motorcycle police officer, the officer starts to accelerate at 1.8m/s^2 to overtake her. Assuming the officer maintains this acceleration, determine the time it takes the police officer to reach the motorist (in seconds).

Homework Equations


vi^2 + 2ad = vf^2
v=at
d=vt

The Attempt at a Solution


Here is what I did I am curious why my method is incorrect.
(14.4)t=d (speeder)
vt=d (officer)
v=at (officer)
at^2=d (officer)

1.8t^2 = 14.4 t
t=0, 8

Correct answer is 16

Ok I realized that d = 1/2 vt^2
this was my mistake, please show mathematically why I can't use these two equations to form d =vt^2

vt=d
vf =at (if vi=0)
(at)t=d
at^2 =d
 
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Yousufshad said:
Ok I realized that d = 1/2 vt^2
this was my mistake, please show mathematically why I can't use these two equations to form d =vt^2

vt=d
vf =at (if vi=0)
(at)t=d
at^2 =d

vt = d only if velocity is constant over time. In this case it is not since there is acceleration involved. So you must turn to the full kinematic expression:

## d(t) = d_o + v_o t + \frac{1}{2} a t^2##
 
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gneill said:
vt = d only if velocity is constant over time. In this case it is not since there is acceleration involved. So you must turn to the full kinematic expression:

## d(t) = d_o + v_o t + \frac{1}{2} a t^2##
Ok, thanks, great to know :)
 
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