Question

a particle is moving along y axis. the position y of particle varies with time t as y = (t3 - t2 + 1) m. the displacement of particle from t =0 to t = 2s is

Answer 1

at t=0 y=1 and at t=2 y=3

Answer 2

The displacement of the particle from t = 0 to t = 2 sec is equal to 4 m.

Given:

Position-time function: y = t³ - t² + 1

To Find:

The displacement of particle from t = 0 to t = 2 second.

Solution:

→ The position-time function for a particle is a function that describes the relationship between the instantaneous position of the particle and time. We can say that the position-time function describes the instantaneous position of a particle as a function of time.

→ Similarly the position-time graph for a particle is the graph between the instantaneous position of the particle and time.

→ In the given question the position-time function is: y = t³ - t² + 1

• Position at time t = 0 second (y₁) = (0)³ - (0)² + 1 = 1 m

• Position at time t = 2 second (y₂) = (2)³ - (2)² + 1 = 8 - 4 + 1 = 5 m

→ For an one dimensional motion we can say that the displacement of the particle is equal to change in its position. If the particle moves from the position y(t₁) to the position y(t₂), then its displacement is y(t₂) − y(t₁) over the time interval [t₁, t₂].

∴ The displacement of the particle will be equal to the change in the position of the particle from t = 0 to t = 2 seconds.

∴ Displacement of the particle = 5 - 1 = 4 m

Hence the displacement of the particle from t = 0 to t = 2 second is equal to 4 m.

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