Physics-
General
Easy

Question

The position of a particle x (in metres) at a time t seconds is given by the relation stack r with rightwards arrow on top equals left parenthesis 3 t stack i with hat on top minus t to the power of 2 end exponent stack j with hat on top plus 4 stack k with hat on top right parenthesis. Calculate the magnitude of velocity of the particle after 5 seconds

  1. 3.55  
  2. 5.03  
  3. 8.75  
  4. 10.44  

The correct answer is: 10.44


    stack r with rightwards arrow on top equals 3 t stack i with hat on top minus t to the power of 2 end exponent stack j with hat on top plus 4 stack k with hat on top
    Velocity, stack v with rightwards arrow on top equals fraction numerator d stack r with rightwards arrow on top over denominator d t end fraction equals fraction numerator d over denominator d t end fraction open parentheses 3 t stack i with hat on top minus t to the power of 2 end exponent stack j with hat on top plus 4 stack k with hat on top close parentheses equals 3 stack i with hat on top minus 2 t stack j with hat on top
    At t equals 5 s rightwards double arrow stack v with rightwards arrow on top equals 3 stack i with hat on top minus 10 stack j with hat on top
    open vertical bar stack v with rightwards arrow on top close vertical bar equals square root of open parentheses 3 close parentheses to the power of 2 end exponent plus open parentheses negative 10 close parentheses to the power of 2 end exponent end root equals square root of 9 plus 100 end root equals square root of 109 equals 10.44 blank m s to the power of negative 1 end exponent

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