State the meaning of velocity.
A car moves in a straight line up a slope, as shown in Fig. 3.1. The car has mass $850\,\text{kg}$ and is travelling at a constant speed of $9.0\,\text{m s}^{-1}$. The car’s engine exerts a force on the car of $2.0\,\text{kN}$ up the slope. A resistive force $F_D$, caused by friction and air resistance, acts against the motion of the car. The way $F_D$ changes with the car’s speed $v$ is shown in Fig. 3.2.
State and explain whether the car is in equilibrium while it moves up the slope.
Look at the forces acting along the slope. Use the information in Fig. 3.2 to find the component of the car’s weight acting down the slope.
Show that the car’s power output is $1.8 \times 10^4\,\text{W}$.
The car now moves along level ground. The output power of the car remains at $1.8 \times 10^4\,\text{W}$. The variation of the resistive force $F_D$ on the car is shown in Fig. 3.2. Calculate the acceleration of the car when its speed is $15\,\text{m s}^{-1}$.