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The magnitude and direction of the instantaneous velocity of the particle at t=0.25 s is 1.5624 m/s and 36.87°.
What is instantaneous velocity?
The time rate of change of velocity at a particular instant of time is called the instantaneous velocity.
Given the position vector of particle moving in xy plane, x =2.5m/s²)t² and y=(5.0m/s³)t³
The instantaneous velocity is v = dx/dt or dy/dt
Instantaneous velocity in x direction v(x) =d/dt(2.5t²) = 5t
At 0.25 sec, Instantaneous velocity in x direction v(x) = 5 x 0.25 = 1.25 m/s
Instantaneous velocity in y direction v(y) =d/dt(5t³) = 15t²
At 0.25 sec, Instantaneous velocity in x direction v(y) = 15 x (0.25)² = 0.9375 m/s
The magnitude of velocity v = √[(v(x)² + v (y)²] = 1.5624 m/s
The direction of velocity is
tan θ= v(y)/v(x)
tan θ= 15t²/5t = 3t
At 0.25 s, tan θ =3 x 0.25 =0.75
θ = tan⁻¹ (0.75) = 36.87°
Thus, magnitude and direction of the instantaneous velocity of the particle at t=0.25 s is 1.5624 m/s and 36.87°.
Learn more about instantaneous velocity.
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