Question

The displacement of a particle which moves along the s-axis is given by; = (−2 + 3)−0.5 Where s is in meters and t is in seconds. Determine the time at which the acceleration is zero.

Answer 1

The time at which the acceleration is zero is given as 4.66 seconds

How to solve for the time

First we have to solve for the velocity. To do this, we would have to take the derivative.

$s = e^-0.5t (3 t - 2)$

Then velocity =

$ds/dt = e^-0.5t (4 - 1.5 t)$

The acceleration can be gotten by finding the second derivative

$a = dv/dt = e^-0.5t (.75 t - 3.5)$

To find t at acceleration = 0

We have

$0 = e^-0.5t (.75t - 3.5)$

This gives t to be

t = 4.66 sec

Complete 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.

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