Particle motion: position, velocity, acceleration practice problems
Position, velocity and acceleration along a line: when the particle stops, which way it moves, and how far it travels. 10 problems with worked solutions; in 10 of them every equation is proved by a computer algebra system.
A particle moves along a line with position \( \displaystyle s(t) = 2 t^{3} - 24 t^{2} + 72 t + 9 \) (meters, \( \displaystyle t \) in seconds). Find its velocity and acceleration, the times it is at rest, and the total distance it travels for \( \displaystyle 0 \le t \le 7 \).
A particle moves along a line with position \( \displaystyle s(t) = 2 t^{3} - 18 t^{2} + 30 t + 4 \) (meters, \( \displaystyle t \) in seconds). Find its velocity and acceleration, the times it is at rest, and the total distance it travels for \( \displaystyle 0 \le t \le 7 \).
A particle moves along a line with position \( \displaystyle s(t) = t^{3} - 9 t^{2} + 24 t + 7 \) (meters, \( \displaystyle t \) in seconds). Find its velocity and acceleration, the times it is at rest, and the total distance it travels for \( \displaystyle 0 \le t \le 5 \).
A particle moves along a line with position \( \displaystyle s(t) = t^{3} - 9 t^{2} + 15 t \) (meters, \( \displaystyle t \) in seconds). Find its velocity and acceleration, the times it is at rest, and the total distance it travels for \( \displaystyle 0 \le t \le 6 \).
A particle moves along a line with position \( \displaystyle s(t) = 2 t^{3} - 24 t^{2} + 72 t + 8 \) (meters, \( \displaystyle t \) in seconds). Find its velocity and acceleration, the times it is at rest, and the total distance it travels for \( \displaystyle 0 \le t \le 8 \).
A particle moves along a line with position \( \displaystyle s(t) = 2 t^{3} - 18 t^{2} + 48 t \) (meters, \( \displaystyle t \) in seconds). Find its velocity and acceleration, the times it is at rest, and the total distance it travels for \( \displaystyle 0 \le t \le 6 \).
A particle moves along a line with position \( \displaystyle s(t) = 2 t^{3} - 24 t^{2} + 90 t + 7 \) (meters, \( \displaystyle t \) in seconds). Find its velocity and acceleration, the times it is at rest, and the total distance it travels for \( \displaystyle 0 \le t \le 6 \).
A particle moves along a line with position \( \displaystyle s(t) = t^{3} - 15 t^{2} + 63 t + 9 \) (meters, \( \displaystyle t \) in seconds). Find its velocity and acceleration, the times it is at rest, and the total distance it travels for \( \displaystyle 0 \le t \le 9 \).
A particle moves along a line with position \( \displaystyle s(t) = t^{3} - 15 t^{2} + 63 t + 1 \) (meters, \( \displaystyle t \) in seconds). Find its velocity and acceleration, the times it is at rest, and the total distance it travels for \( \displaystyle 0 \le t \le 8 \).
A particle moves along a line with position \( \displaystyle s(t) = 2 t^{3} - 24 t^{2} + 90 t + 7 \) (meters, \( \displaystyle t \) in seconds). Find its velocity and acceleration, the times it is at rest, and the total distance it travels for \( \displaystyle 0 \le t \le 7 \).