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Distance-Time Graphs

particle as a...

Question

In figure shows the x coordinate of a particle as a function of time. Find the signs of v_x and a_x at t = t₁, t = t₂ and t = t₃.

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Solution

Slope of the x–t graph gives the velocity and change in the slope gives the acceleration.
At t = t₁,
Slope = Positive ⇒ Velocity = Positive
Slope is increasing ⇒ Acceleration = Positive

At t = t₂,
Slope = Zero ⇒ Velocity = Zero
Slope is increasing ⇒ Acceleration = Negative

At t = t₃,
Slope = Negative ⇒ Velocity = Negative
Slope is increasing ⇒ Acceleration = Positive

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