Question

A particle moves along the x axis. Its position is given by the equation

Answer 1

The position of the particle when it changes direction is x = 3.0 m

Explanation:

The position of the particle is given by the equation

$x(t)=2.4+2.9t-3.5t^2$

In order to determine its position when it changes direction, we need to  find the time t at which the velocity of the particle becomes zero.

The velocity of the particle si given by the derivative of the position, therefore:

$v(t)=\frac{dx}{dt}=2.9-2\cdot 3.5t^{2-1}=2.9-7t$

The velocity is zero when:

$v(t)=0=2.9-7t\\7t=2.9\\t=\frac{2.9}{7}=0.41 s$

And therefore, the position at t = 0.41 s is

$x(0.41)=2.4+2.9(0.41)-3.5(0.41)^2=3.0 m$

Learn more about position and velocity:

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