Question

classify the following scenarios as accelerating or not accelerating.
a kid jumping up and down
a satellite orbiting earth at a rate of 3.07 km/s
an ice skater skating in a straight line at a constant
a car slowing down and coming to a stop

Explanation:

Step1: Analyze each scenario

• For a kid jumping up and down:
• When jumping up, the kid is moving against gravity (decelerating), at the highest point velocity is \(0\), and when coming down, the kid is accelerating due to gravity. So there is a change in velocity (either magnitude or direction), so it is accelerating.
• For a satellite orbiting Earth at a rate of \(3.07\) km/s:
• The satellite is moving in a circular path. In circular motion, the direction of velocity is constantly changing (even if the speed is constant). Since acceleration is the rate of change of velocity (which has both magnitude and direction), a satellite in circular orbit is accelerating.
• For an ice - skater skating in a straight line at a constant speed:
• Velocity (which is speed in a particular direction) has a constant magnitude and direction. The formula for acceleration \(a=\frac{\Delta v}{\Delta t}\), where \(\Delta v = v_{final}-v_{initial}\). Since \(v_{final}=v_{initial}\), \(a = 0\). So it is not accelerating.
• For a car slowing down and coming to a stop:
• The speed (magnitude of velocity) is decreasing. Using the formula \(a=\frac{v - u}{t}\) (where \(v\lt u\)), the acceleration is negative (but still non - zero). So it is accelerating.

Answer:

Accelerating: A kid jumping up and down, A satellite orbiting Earth at a rate of \(3.07\) km/s, A car slowing down and coming to a stop
Not Accelerating: An ice - skater skating in a straight line at a constant speed