PHY131H1 physics tutoring at U of T St George

The stated force is already the net force. First use $F_{\mathrm{net}}=ma$ with the chosen positive direction, then update the velocity before deciding whether the cart reverses.

1. Use the net force to find acceleration

   The net force is negative because it points left: $F_{\mathrm{net}}=-0.50\,\mathrm{N}$. Newton’s second law gives

   $$\begin{aligned}a&=\frac{F_{\mathrm{net}}}{m}\\&=\frac{-0.50}{0.50}\\&=-1.0\,\mathrm{m/s^2}.\end{aligned}$$

   The force is already the net force; do not subtract another friction force.

2. Update the velocity

   A constant net force on a constant mass gives constant acceleration. Therefore

   $$\begin{aligned}v&=v_0+at\\&=4.0+(-1.0)(2.0)\\&=+2.0\,\mathrm{m/s}.\end{aligned}$$

   The positive sign means the cart is still moving right.

3. Find and interpret the displacement

   For constant acceleration, average velocity is $(v_0+v)/2=(4.0+2.0)/2=3.0\,\mathrm{m/s}$. Hence

   $$\begin{aligned}\Delta x&=v_{\mathrm{average}}\Delta t\\&=3.0\times2.0\\&=+6.0\,\mathrm{m}.\end{aligned}$$

   The displacement is 6.0 m to the right.

4. Check the direction over the whole interval

   The velocity decreases steadily from $+4.0$ to $+2.0\,\mathrm{m/s}$, so it stays positive throughout. The cart slows down without reversing.

   If the same force continued, it would stop momentarily at $4.0\,\mathrm{s}$ and move left afterward. That extension is outside the stated interval.

   Acceleration points toward the change in velocity. It does not have to point in the direction the object is currently moving.