Final answer:
A pencil on a car dashboard will slide forward when the car suddenly stops and slide backward when it accelerates due to inertia. To calculate stopping time and distance, one would need additional information and could use kinematic equations to determine these values, including the car's initial velocity.
Step-by-step explanation:
When a car suddenly stops, a pencil lying on the dashboard will slide forward due to inertia, according to Newton's first law of motion. Similarly, when a car suddenly accelerates, the pencil will slide backward, again due to inertia. The reason for this is that the pencil tends to maintain its state of motion (or rest) unless acted upon by a net external force, which in this case is the frictional force of the dashboard and the force exerted by the car's sudden stop or acceleration.
To determine how long it takes for the car to stop completely, the distance the car travels in this time, and the car's initial velocity, one needs additional data. However, if we assume a deceleration rate (negative acceleration), initial speed, and the time the car takes to stop, we can use kinematic equations to find these values. For example, using the formula final velocity = initial velocity + (acceleration × time) and knowing that the final velocity is zero when the car stops, we can rearrange to find initial velocity or time if the other values are known.