Forces and Newton’s Laws: Question 4

Worked solution

Part (a): Resultant force

The driving force and the resistive force act along the same line but in opposite directions, so subtract to find the resultant:

$\text{Resultant force} = 640\text{ N} - 100\text{ N} = \boxed{540\text{ N}}$

This resultant force acts forward, in the direction the go-kart is already travelling, since the driving force is bigger than the resistive force.

Part (b): Acceleration

Use $F = ma$, where $F$ is the resultant force found in part (a):

$F = ma \quad\Rightarrow\quad a = \frac{F}{m}$

$a = \frac{540\text{ N}}{180\text{ kg}}$

$a = \boxed{3.0\text{ m/s}^2}$

Part (c): Direction of the acceleration

The equation $F = ma$ tells us that the resultant force and the acceleration it produces are always in the same direction. Since the resultant force found in part (a) acts forward, the acceleration also acts forward. In the direction the go-kart is moving. This is why the go-kart speeds up rather than slows down.

Part (d): Removing the driving force

Once the driving force is removed, the only force left acting along the go-kart’s direction of motion is the resistive force of $100\text{ N}$, and this now acts backward (opposing the motion, as resistive forces always do).

Since this is now the resultant force, by $F = ma$ it produces a backward acceleration. That is, a deceleration. The go-kart’s speed steadily decreases, rather than stopping instantly, because the resistive force (unlike a sudden brake) only produces a gradual change in speed.

Final answers

• (a) Resultant force $=$ $540\text{ N}$ forward
• (b) Acceleration $=$ $3.0\text{ m/s}^2$
• (c) Acceleration acts forward, in the same direction as the resultant force
• (d) The go-kart decelerates (slows down), because the resistive force now acts as an unbalanced backward force