A mass is moving with constant acceleration in the xy plane

A mass is moving with constant acceleration in the x-y plane. At time t = 0s the mass’s position is 6m ^i + 8mˆ, the mass’s velocity is 4 m s ˆ + 3m s ˆ and the mass is subject to an acceleration of 1 m s 2 ˆ 3 m s 2 ˆ.

16. Which unit vector describes the direction of the velocity when the x-component of position is a maximum?

17. At what time is the velocity perpendicular to the acceleration?

Solution

position of mass at t=0: r = 6 m ^i + 8 mjˆ

velocityof mass at t=0: v =4 m/ s ˆ + 3m/ s jˆ

acceleration of mass at t=0: a = 1 m/s² ˆ 3 m/s² jˆ

16.

when the x-component of the position is maximum, the velocity along the x-direction is zero.

this means that the velocity is directed in y-axis. So, the unit vector of positon indicates the

direction of the velocity. In this case, the velocity has only y-component.

the velocity v =4 m/ s ˆ + 3m/ s jˆ, if the x-component of the position is maximum, we have

only y-component of the velocity: that is,

  v = + 3m/s jˆ

so, the velocity is directed in +y direction.