Question

A particle moves in 2 d motion such that it's position depends on x=4t2+2t+3 y=5t+7 then find the velocity at t=2 sec and find the angle between vx and vy

Answer 1

Dear student,

Given :-

• position x = 4t² + 2t + 3
• position y = 5t + 7
• object undergoes 2-D motion
• time at which velocity is to be found = 2 sec

To find :-

• Velocity at t = 2 sec
• Angle between vx and vy.

Solution :-

For the position x, differentiating with respect to time, we get;

             x = 4t² + 2t + 3

      dx/dt = 4t² + 2t + 3

             v = 8t + 2

             v = 8(2) + 2

             v = 16 + 2

            v = 18 m/s i

For position y, differentiating with respect to time, we get;

             y = 5t + 7

      dy/dt = 5t + 7

            v = 5 m/s j

Now, taking the magnitude of the velocity to conclude about the value of velocity as;

        |v| = √(18² + 5²)

             = √324 + 25

             = √349

            ≈ 18.68 m/s

Nothing much sure can be said about the angle between Vx and Vy.