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Question

The distance traveled s (in metres) by a particle in t seconds is given by s=t3+2t2+1. The speed of the particle after 1second will be


A

8cm/sec

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B

6cm/sec`

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C

2cm/sec

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D

None of these

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Solution

The correct option is D

None of these


Step 1: Given data

Distance traveled by particle=s

Time is taken to travel a distance=t

Relation between s and t, s=t3+2t2+1

Step 2: Formula used

We know that the dsdt will give us the expression for the speed v of the particle at any time t. So,

v=dsdt

Step 3: Speed of particle at a time t

Using the formula to differentiate distance with respect to time-

s=t3+2t2+tdsdt=3t2+4t+1dsdtt=1=3×12+4×1+1dsdtt=1=8m/sec

Thus, the speed of the particle after 1second will be 8m/sec.

Hence, option D is the correct answer.


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