AP EAMCET · PHYSICS · Motion In One Dimension

The displacement of a particle moving with uniform acceleration in time $t$ is given by $S = 30 t + 5 t^{2}$ , its initial velocity is _____

A $35 m s^{- 1}$
B $30 m s^{- 1}$
C $40 m s^{- 1}$
D $45 m s^{- 1}$

Verified Solution

Answer & Solution

Correct Answer

(B) $30 m s^{- 1}$

Step-by-step Solution

Detailed explanation

Given that displacement S=30t+5t2 Velocity is given by v=dsdt ⇒v=d30t+5t2dt ⇒v=30+10t Initial velocity at t=0 v=30+100=30 m s-1

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

Same subject

Explore more questions on app

From AP EAMCET

Explore more questions on app

The displacement of a particle moving with uniform acceleration in time t is given by S=30t+5t2, its initial velocity is _____

Step-by-step Solution

The displacement of a particle moving with uniform acceleration in time $t$ is given by $S = 30 t + 5 t^{2}$ , its initial velocity is _____