Question

a. At this instant, is the particle in FIGURE Q4.2 speeding up, slowing down, or traveling at constant speed?

b. Is this particle curving upward, curving downward, or traveling straight?

Short answer

a. The particle is traveling with a constant speed.

b. The particle is curving downward.

Step-by-step solution

Step.1.

Acceleration: rate of change of velocity with respect to time is known as acceleration. The formula to find the instantaneous acceleration is as follows,

$\overrightarrow{a}=\frac{d\overrightarrow{v}}{dt}$

Here $\overrightarrow{a}$is the instantaneous acceleration, dv is small change in velocity and dt is the small change in time.

Part.(a)

Consider the following diagram,

The velocity component v and acceleration component $\overrightarrow{a}$ are right angle to each other. A component of the acceleration parallel and in the same direction of velocity would speed up the particle but a component of the acceleration parallel and in the opposite direction of velocity would slow down the particle, respectively. Since there is no any parallel component of acceleration, the speed is not changing. Therefore the particle is traveling with a constant speed.

Part.(b)

The velocity of the particle is towards left and the acceleration is downwards so the particle takes a parabolic path in the downward direction. Therefore the particle is curving downward. The path of the particle is shown below.