The displacement of a particle which moves along the s-axis isgiven by s = (-2+3

Question

The displacement of a particle which moves along the s-axis isgiven by s = (-2+3t)e^(-0.5t), where s is in meters and t is inseconds. Plot the displacement, velocity and acceleration versustime for the first 20 seconds of motion. Determine the time atwhich the acceleration is zero. The displacement of a particle which moves along the s-axis isgiven by s = (-2+3t)e^(-0.5t), where s is in meters and t is inseconds. Plot the displacement, velocity and acceleration versustime for the first 20 seconds of motion. Determine the time atwhich the acceleration is zero.

Explanation / Answer

Take the derivative of displacement to get velocity, take thesecond derivative to get acceleration: Velocity = v = ds/dt = e^-0.5t (4 - 1.5 t) Acceleration = a = dv/dt = e^-0.5t (.75 t - 3.5) To find the time (t) when a = 0, Set the acceleration equationequal to zero and solve for t: 0 = e^-0.5t (.75t - 3.5) t = 4.66 sec
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