An astronaut on board a spacecraft is in orbit around the earth in uniform circular motion.
Is her velocity speed and acceleration constant?
Both velocity and acceleration are vectors. Vectors have magnitude and DIRECTION.
Their magnitudes may stay the same, speed may be constant tangential to orbit path and acceleration magnitude toward earth.
HOWEVER
The velocity and acceleration DIRECTIONS change constantly, so the vectors are NOT constant.
Speed is a magnitude.
Velocity is a VECTOR.
Remember:
In a car you can measure speed with a speedometer.
but
for velocity you need both a speedometer and a compass.
Speed is the magnitude of the velocity vector, a scalar.
In this scenario, the astronaut's velocity and speed are not constant, but her acceleration is constant. Let me explain why:
Velocity is a vector quantity that includes both speed and direction. In uniform circular motion, the object (in this case, the spacecraft) moves in a circular path at a constant speed. However, since the object is constantly changing direction, the velocity is changing as well.
Acceleration, on the other hand, is the rate of change of velocity. In uniform circular motion, the object is constantly changing direction, which means it is experiencing an acceleration. This acceleration is directed towards the center of the circular path and is commonly referred to as centripetal acceleration.
To calculate the magnitude of the centripetal acceleration, we can use the formula:
a = (v^2) / r,
where "a" represents the centripetal acceleration, "v" represents the velocity (constant speed), and "r" represents the radius of the circular path.
So, in summary, the astronaut's velocity (combination of speed and direction) is not constant because the direction is continuously changing, but the acceleration (centripetal acceleration) remains constant as long as the speed and radius of the orbit remain constant.