Question

a car is driving around a curved part of a road as shown below;
the dots in the diagram show the location of the car every 1 sec drives around the curve. they are equal distances apart.
consider the car’s motion when it’s at the position shown in the
complete the statement below.

• the car dropdown accelerating. this must be true because it is dropdown with options: speeding up, moving at a constant speed, changing direction.

Explanation:

To determine the car's acceleration, we analyze its motion:

1. Acceleration Definition: Acceleration occurs when there's a change in velocity (speed or direction).
2. Direction Change: The car is moving along a curved path. Any object moving in a curve is constantly changing its direction of motion (velocity is a vector, so direction change means velocity change).
3. Constant Speed?: The dots are equally spaced, meaning the car covers equal distances in equal time intervals (1 second each), so its speed (magnitude of velocity) is constant. But since direction is changing, velocity is changing.
4. Conclusion on Acceleration: Since velocity (direction) is changing, the car is accelerating. The reason is that it is changing direction (and also, if we consider the curved path, even with constant speed, direction change causes acceleration; however, the options here include "changing direction" as a reason, and also note that if speed were changing, "speeding up" would apply, but dots are equally spaced so speed is constant. So the car is accelerating because it is changing direction (and also, technically, centripetal acceleration exists for circular/curved motion, but the options here focus on direction change or speed change).

For the first blank: The car is accelerating (because direction change causes velocity change, hence acceleration).
For the second blank: The reason is changing direction (since speed is constant, as dots are equally spaced, so "speeding up" is incorrect; "moving at constant speed" is true about speed, but the reason for acceleration is direction change).

Answer:

• The car \(\boldsymbol{\text{is}}\) accelerating. This must be true because it is \(\boldsymbol{\text{changing direction}}\) (and also, even with constant speed, direction change means velocity change, hence acceleration).

(Note: The first dropdown should have "is" (since acceleration occurs due to direction change), and the second dropdown should have "changing direction" (as speed is constant, so "speeding up" is wrong, and "changing direction" is the correct reason for acceleration here).)