Acceleration

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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?