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A curvilinear motion of a particle is defined by $V_X=25-8t$ m/s andy$=48-3t^2$ m. At t = 0, x = 0. Find out position, velocity and acceleration at t = 4 sec.
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Horizontal motion

$ V_x=25-8t ----------(i) \\ \therefore V_{x_{t=4}}=25-8×4 \\ \therefore V_x=-7m/s \\ x=∫_0^4 (25-8t)dt \space \space [\because at t=0, x=0] \\ =[25t-4t^2]_0^4 \\ x=38m \\ a_x=\dfrac {dV_x}{dt}=0-8 \\ a_x=-8m/s^2$

Vertical motion

$ y=48-3t^2 \\ At t=4, \\ y=48-3(4)^2 \\ y=0 \\ V_y= \dfrac {dy}{dt}=48-6t \\ At t=4, \\ V_y=48-6(4) \\ \therefore V_y=24m/s \\ a_y= \dfrac {dV_y}{dt}=0-6 \\ \therefore a_y=-6m/s^2 $

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