It may seem mundane: having a relative drive you around to do errands.

But to the tennis champion Serena Williams, a decision to let her 18-year-old nephew drive her to meetings so that she could safely use her phone in the car filled her with misgivings that go to the heart of the national discourse on race and policing.

In a social media post on Tuesday, Ms. Williams described how spotting a police officer on the side of the road during her ride with a young black man at the wheel inspired thoughts of life and death.

“I quickly checked to see if he was obliging by the speed limit,” Ms. Williams wrote on her public Facebook page. “I remembered that horrible video of the woman in the car when a cop shot her boyfriend.

“All of this went through my mind in a matter of seconds,” she wrote. “I even regretted not driving myself. I would never forgive myself if something happened to my nephew.”

The “woman in the car” was mostly likely a reference to the girlfriend of Philando Castile, a 32-year-old school cafeteria worker who was at the wheel when he was pulled over in July by a Hispanic police officer in a Minnesota suburb, ostensibly for a cracked taillight. He was shot and killed while reaching for his identification.

His girlfriend, Diamond Reynolds, who was at his side while her young daughter sat in the back seat, posted a video of the harrowing encounter on Facebook Live.

Mr. Castile had been pulled over by the police in the Minneapolis-St. Paul region at least 49 times in a 13-year span, often for minor infractions: turning into a parking lot without signaling; failing to repair a broken seatbelt; driving at night with an unlit license plate; driving with tinted windows.

His death came amid a period of violent protests after the police killings of black men across the nation and counterattacks that saw gunmen take the lives of officers in Dallas and Baton Rouge, La. On Tuesday, the fatal police shooting of a black man in El Cajon, Calif., who the authorities said had pointed an object at officers, was the latest flash point.

As a high-profile athlete, Ms. Williams used the weight of her celebrity to convey the despair that has gripped many black Americans after multiple police killings, most of them men. Her post also highlighted the awareness of black Americans that they are often regarded with suspicion by the authorities during everyday activities.

The cognizance, which many say is nothing new but is being talked about more frequently because of the national discussion on police shootings, has bred movements like Black Lives Matter and hashtag trends like #shoppingwhileblack.

Research has shown that black Americans are more likely to be stopped by the police than whites and are more likely to be touched, handcuffed, pushed to the ground or pepper-sprayed by an officer after being stopped.

It is a trend underscored by frequency and longevity, activists say. Back in 2009, when the well-known Harvard professor Henry Louis Gates Jr. was confronted by a Cambridge, Mass., police officer while trying to open his jammed front door, it spurred a national discussion of racial profiling and a White House “beer summit,” in which President Obama invited Mr. Gates and the officer to discuss the encounter.

The roster of black victims since then has included Michael Brown, Eric Garner, Sandra Bland, Keith Scott, Tamir Rice.

The awareness that young black people in particular must be given extra coaching to avoid seeming suspicious while going about their daily lives is a concern of parents, educators and activists. Last month, for example, a 15-year-old black girl who collided with a car while riding a bicycle in Maryland was handcuffed and pepper sprayed by the police as they tried to take her into custody.

On Monday, the N.B.A. star LeBron James said that his son would start driving his own car in four years, but that he was afraid for him already. (A New York Times examination of traffic stops and arrests in Greensboro, N.C., in 2013, for example, showed officers pulled over African-American drivers at a rate far out of proportion with their share of the local driving population.)

“It’s a scary thought right now to think if my son gets pulled over, and you tell your kids if you just [comply] and you just listen to the police that they will be respectful and things will work itself out,” he said, according to ABC News.

He added that he was “not that confident that things are going to go well and that my son is going to return home.”

The N.F.L. quarterback Colin Kaepernick, who has been vociferously criticized for protesting racial injustice by taking a knee during the national anthem and has been joined by other sports figures, published a video on Instagram on Wednesday that he described as “painful to watch.”

It was of Zianna Oliphant, a 9-year-old girl from Charlotte, N.C., speaking at a City Council meeting on Monday after the fatal police shooting of Keith Lamont Scott.

“I feel like that we are treated differently than other people,” she said, pausing tearfully.

“We are black people and we shouldn’t have to feel like this. We shouldn’t have to protest because you all are treating us wrong. We do this because we need to and have rights.

“I’ve been born and raised in Charlotte and I never felt this way until now,” she said.

“It is a shame that our fathers and mothers are killed and we can’t even see them anymore. It’s a shame that we have to go to the graveyard and bury them. We have tears and shouldn’t have tears.”

Ms. Williams, who signed off her Facebook post with the words, “I Won’t Be Silent,” noted that her nephew was “so innocent,” but so were “the others.”

“I am a total believer that not ‘everyone’ is bad,” she wrote. “It is just the ones that are ignorant, afraid, uneducated and insensitive that is affecting millions and millions of lives. Why did I have to think about this in 2016?”