Question

Velocity of a particle depends on time as v=3t^2+5
find the displacement equation of particle
also find acceleration at time t=3sec

Answer 1

Answer:

$\bf \odot \: \bf \: Displacement \: s =42 \: m \\ \bf \odot \: \bf \: Acceleration \: a = \: 18 \: m {s}^{ - 2}$

Step-by-step explanation:

Given,

$\sf \: v = 3 {t}^{2} + 5$

To find :

1. Displacement (s)
2. Acceleration (a)

Solution :

1)

To find displacement we have to integrate velocity.

$\sf \: s = \displaystyle \int \sf \: v \: \: dt \\ = \displaystyle \int \sf \: ( 3 {t}^{2} + 5 )\: \: dt \\ = 3 \frac{ {t}^{3} }{3} + 5t \\ = {t}^{3} + 5t \\ \\ \sf \: at \: \: \: t \: = 3 \: s \\ \sf \: displacement \: \: s = {3}^{3} + 5 \times 3 \\ = 27 + 15 \\ = 42 \: m$

2)

To find acceleration we have to differentiate velocity.

$\sf \: acceleration \: \: \: a \: = \frac{dv}{dt} \\ \sf \: = \frac{d}{dt} (3 {t}^{2} + 5) \\ = 3 \times 2t + 0 \\ = 6t \\ \\ \sf \: at \: \: \: t = 3 \: s \: \\ \sf \: accelration \: \: \: a = 6 \times 3 \\ = 18 \: m {s}^{ - 2}$

Answer 2

Answer:

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