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Question: The displacement is given by \(x = 2 t ^ { 2 } + t + 5\) , the acceleration at \(t = 2 s\) is...

The displacement is given by x=2t2+t+5x = 2 t ^ { 2 } + t + 5 , the acceleration at t=2st = 2 s is

A

4 m/s24 \mathrm {~m} / \mathrm { s } ^ { 2 }

B

8m/s28 m / s ^ { 2 }

C

10 m/s210 \mathrm {~m} / \mathrm { s } ^ { 2 }

D

15 m/s215 \mathrm {~m} / \mathrm { s } ^ { 2 }

Answer

4 m/s24 \mathrm {~m} / \mathrm { s } ^ { 2 }

Explanation

Solution

Displacement x=2t2+t+5x = 2 t ^ { 2 } + t + 5

Velocity =dxdt=4t+1= \frac { d x } { d t } = 4 t + 1

Acceleration =d2xdt2=4= \frac { d ^ { 2 } x } { d t ^ { 2 } } = 4 i.e. independent of time

Hence acceleration =4m/s2= 4 m / s ^ { 2 }