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The acceleration of a particle which is ...

The acceleration of a particle which is depend on time is given by following function a = 2t + 1 and at time t = 0, x = 1m and ui = 2m/s. Then find out displacement of the particle at t = 3 sec.

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To solve the problem, we need to find the displacement of a particle given its acceleration as a function of time, initial position, and initial velocity. Here’s a step-by-step solution: ### Step 1: Understand the given information - Acceleration \( a(t) = 2t + 1 \) - Initial position \( x(0) = 1 \, \text{m} \) - Initial velocity \( u = 2 \, \text{m/s} \) - Time \( t = 3 \, \text{s} \) ...
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Knowledge Check

  • The displacement of a particle in time t is given by s=2t^2-3t+1 . The acceleration is

    A
    1
    B
    3
    C
    4
    D
    5

  • The acceleration a of alpha of a particle depends on displacements covered in a time t as a= S + 5 . It is given that initially S=0 m and v=5m//s . Then

    A
    `v= S+5`
    B
    `v= sqrt(S+5)`
    C
    `t= log_(e)((S+5)/(S))`
    D
    `t= log_(e)((S+5)/(5))`

  • A starts from rest, with uniform acceleration a. The acceleration of the body as function of time t is given by the equation a = pt, where p is a constant, then the displacement of the particle in the time interval t = 0 to t=t_(1) will be

    A
    `(1)/(2)pt_(1)^(3)`
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