a(t)
Definition
The term "a(t)" represents the acceleration of an object at a specific time. It measures how quickly the velocity of an object is changing.
Analogy
Think of a car accelerating from 0 to 60 mph. The rate at which the car's speed increases is its acceleration. If the car accelerates rapidly, it will reach 60 mph in a short amount of time.
Related terms
v(t): This term refers to the velocity of an object at a specific time. It measures how fast and in which direction an object is moving.
s(t): This term represents the position or displacement of an object at a specific time. It tells us where the object is located relative to its starting point.
j(t): Also known as jerk, this term describes how quickly acceleration changes over time. It quantifies how uncomfortable or smooth an object's motion feels.
"a(t)" appears in:
Study guides (2)
Practice Questions (4)
- A soccer player kicks a ball in a straight line. The position of the ball as a function of time is given by *s(t) = t^2 - 3t + 1*. What is a(t), the acceleration of the ball as a function of time?
- The total assets of a stock trader can be modeled by A(t)=1000-t^3. What is the second derivative of the assets with respect to time.
- The amount of money in a savings account is given by the function A(t), where t is measured in years and A is measured in dollars. The rate of change of money is proportional to the square root of the current amount of money. When the account contains $10,000, the amount of money is increasing at $1,000/year. What is the differential equation that represents this situation?
- The rate of change of the surface area of a sphere with respect to time is proportional to the square of the radius. At t = 0, the radius is 2 cm, and the rate of change of the surface area is 16 cm^2/s. If A(t) is the surface area of the sphere, what is the differential equation that represents this situation?
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