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Standard XII

Physics

Displacement in 2D Motion

Let the insta...

Question

Let the instantaneous velocity of a rocket just after launching, be given by the expression $v = 2 t + 3 t^{2}$ (where $v$ is in $m s^{- 1}$ and $t$ is in seconds). Find out the distance travelled by the rocket from $t = 2 s$ to $t = 3 s$ .

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Solution

To find the distance travelled, we need to integrate $v$ . [The limits of integration will be from $2 s$ to $3 s$ as we have to find the distance travelled between $t = 2 s$ and $t = 3 s$ .
$x = \int_{2}^{3} v d t = \int_{2}^{3} (2 t + 3 t^{2}) d t = {∣ ∣ ∣ \frac{2 t^{2}}{3} + \frac{3 t^{3}}{3} ∣ ∣ ∣}_{2}^{3}$
$= | t^{2} + t^{3} |_{2}^{3} = 24 m$ .

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Let the instantaneous velocity of a rocket just after launching, be given by the expression v=2t+3t2 (where v is in ms−1 and t is in seconds). Find out the distance travelled by the rocket from t=2 s to t=3 s.

To find the distance travelled, we need to integrate v. [The limits of integration will be from 2 s to 3 s as we have to find the distance travelled between t=2s and t=3s.x=∫32vdt=∫32(2t+3t2)dt=∣∣∣2t23+3t33∣∣∣32=|t2+t3|32=24 m.

Let the instantaneous velocity of a rocket just after launching, be given by the expression $v = 2 t + 3 t^{2}$ (where $v$ is in $m s^{- 1}$ and $t$ is in seconds). Find out the distance travelled by the rocket from $t = 2 s$ to $t = 3 s$ .