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A particle moves along the
x-axis so that at time
t >= 0 its velocity is given by
v(t)=-2t+6. Determine if the particle is moving to the right or to the left at
t=10.

A particle moves along the $x$ -axis so that at time $t \geq 0$ its velocity is given by $v(t)=-2 t+6$ . Determine if the particle is moving to the right or to the left at $t=10$ .

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Relate position, velocity, speed, and acceleration using derivatives

Full solution

Q. A particle moves along the

x

-axis so that at time

t \geq 0

its velocity is given by

v(t)=-2 t+6

. Determine if the particle is moving to the right or to the left at

t=10

.

Identify function and time: Identify the given velocity function and the specific time at which we need to determine the direction of the particle's movement. $\newline$ The velocity function is $v(t) = -2t + 6$ , and we need to find the direction of movement at $t = 10$ .
Find velocity at $t=10$ : Plug the value of $t$ into the velocity function to find the velocity at that time. $v(10) = -2(10) + 6 = -20 + 6 = -14$
Interpret velocity sign: Interpret the sign of the velocity to determine the direction of the particle's movement. $\newline$ Since $v(10) = -14$ , which is negative, the particle is moving to the left on the x-axis at $t = 10$ .

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