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Problems for Position, Velocity, and Acceleration in One Dimension

Problems for Position, Velocity, and Acceleration in One Dimension

Problems for Position, Velocity, and Acceleration in One Dimension

Problems for Position, Velocity, and Acceleration in One Dimension

Problems for Position, Velocity, and Acceleration in One Dimension

Problems for Position, Velocity, and Acceleration in One Dimension

Problem : Find the derivative of f (x) = 3x 4 -2x 2 +5x -1 and evaluate it at x = 2 .

Using the basic calculus rules established in this section, we find that

f'(x) = 12x 3 -4x - 5x -2 andf'(2) = 96 - 8 - 5/4 = 86 + 3/4

Problem : Find the velocity and acceleration functions corresponding to the position function x(t) = 3t 2 - 8t + 458 .

v(t) = x'(t) and a(t) = v'(t) = x''(t) , so using our basic calculus rules again we find that

v(t) = 6t - 8 and a(t) = 6

Notice that the acceleration in this case is constant, and that its value is equal to twice the coefficient of t 2 in x(t) .

Problem : What happens when a car which is traveling along at constant velocity screeches to a halt?

The velocity of the car decreases rapidly, corresponding to a large negative acceleration (or deceleration) of the vehicle (courtesy of good brakes). While the car was traveling at constant velocity, on the other hand, the acceleration was zero.