Acceleration
Definition
Acceleration refers to the rate at which an object's velocity changes over time. It measures how quickly an object is speeding up, slowing down, or changing direction.
Analogy
Think of acceleration like a car's gas pedal. When you press on the gas pedal, the car accelerates and its speed increases. Similarly, when an object experiences acceleration, its velocity changes and it moves faster.
Related terms
Velocity: Velocity is the rate at which an object's position changes over time. It includes both speed and direction.
Deceleration: Deceleration is a type of acceleration that occurs when an object slows down or decreases in speed.
Instantaneous Acceleration: Instantaneous acceleration refers to the acceleration of an object at a specific moment in time. It can be positive (speeding up) or negative (slowing down).
"Acceleration" appears in:
Study guides (3)
Additional resources (2)
Practice Questions (7)
An astronaut visiting a foreign planet throws a bowling ball vertically; he observes it falling with the velocity function given by *v(t) = 4 - 6t*. What is a(t), the acceleration of the bowling ball as a function of time?
A particle moves along the x-axis. Which of the following statements about its position, velocity, and acceleration are correct?
The acceleration of a racing car is proportional to the position of the car times the time passed. After 2 seconds, the car has traveled 12 meters and the acceleration is 6 meters per second per second. If x(t) is the position of the car, what is the differential equation that represents the situation?
If the velocity function of a car is v(t) = 3e^t + 2, what is the acceleration of the car at t = 1?
If the velocity function of a ball is v(t) = 5t^2 + 2t, what is the acceleration of the ball at t = 2?
A particle's position as a function of time (t) is given by the vector-valued function r(t) = <t^3 - 2t, 2t^2 + 3t>. Find the acceleration vector-valued function, a(t), of the particle.
What does the indefinite integral of the acceleration vector-valued function with respect to time give us?
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