Question

A particle is traveling along a straight path described as = 0.75x. If its position along the x-axis is x=(8t)m, where t is in seconds, determine its speed when t=2s.

Answer 1

If

$x=8t (m),$

then

$v_x=dx/dt=8 (m/s).$

From the picture:

$v=v_x/cos⁡α .$

If the particle is travelling along a straight path $y=0.75x$ , then $tan⁡α=0.75.$ In this case . $α=atan⁡0.75≈36.87°.$

$v=8/cos⁡(36.87°) ≈8/0.8=10 (m/s) .$

Answer: $v=10 (m/s)$