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Math Help - Distances and velocities

  1. #1
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    Distances and velocities

    A particle starts from rest at O and travels to A. The journey from O to A takes 25 seconds. The particle reaches A with a speed of 15ms. the velocity of the particle t seconds after it leaves 0 is vms. It is given that v=kt

    Find the distance O to A

    Find the distance of the particle from 0 when its acceleration is 0.72m/s/s

    thanks for any help
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  2. #2
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    Distance and velocity

    Hello gracey
    Quote Originally Posted by gracey View Post
    A particle starts from rest at O and travels to A. The journey from O to A takes 25 seconds. The particle reaches A with a speed of 15ms. the velocity of the particle t seconds after it leaves 0 is vms. It is given that v=kt
    Quote Originally Posted by gracey View Post


    Find the distance O to A

    Find the distance of the particle from 0 when its acceleration is 0.72m/s/s

    thanks for any help
    First, find the value of k using the fact that when t = 25, v = 15.

    Then, writing the velocity as \frac{ds}{dt} (where s is the distance of the particle from O), solve the equation \frac{ds}{dt}= kt^2 by integration, using your value of k.

    You know that when t = 0, s = 0; and you need the value of s when t = 25.

    For the last part, the acceleration is a = \frac{dv}{dt}. So if you differentiate v = kt^2, you'll get a formula for a in terms of t. Use this to find t when a = 0.72; then plug this value of t into your equation for s to find the distance from O.

    Can you complete it now?

    Grandad
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