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Position and velocity at time t under a given force or acceleration vector

This type of question, asked 2 times: 27 Jan 2024, 21 Jan 2026 S1. All 2 questions below, oldest first.

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  1. Question 1

    27 Jan 2024

    21
    A particle starts from origin at t=0t= 0 with a velocity 5i^m/s5\widehat{i}m/s and moves in x−yx - y plane under action of a force which produces a constant acceleration of (3i^+2j^)m/s2(3\widehat{i}+ 2\widehat{j})m/s^{2}. If the xx-coordinate of the particle at that instant is 84 m84\text{ }m, then the speed of the particle at this time is αm/s\sqrt{\alpha}m/s. The value of α\alpha is ________ .

  2. Question 2

    21 Jan 2026 S1

    6
    A 4 kg mass moves under the influence of a force F→=(4t3i^−3tj^)N\overrightarrow{F}=\left( 4t^{3}\widehat{i}- 3t\widehat{j} \right)N where tt is the time in second. If mass starts from origin at t=0t = 0, the velocity and position after t=2 st = 2\text{ }s will be :

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