Question

Position (x) depends on time (t) as :
x=t³-t²
Find acceleration at t= 2

Options
1. 10
2. 8
3. 4
4. 12​

Answer 1

GiveN :

• Position of a object depends on x(t) = t³ - t²

To FinD :

• Acceleration at t = 2 s

SolutioN :

Take given equation :

$\longrightarrow \sf{x \: = \: t^3 \: - \: t^2} \\ \\ \small{\sf{\: \: \: \: \: \: \: \: Differentiate \: wrt. \: t}} \\ \\ \longrightarrow \sf{\dfrac{dx}{dt} \: = \: \dfrac{d(t^3 \: - \: t^2)}{dt}} \\ \\ \longrightarrow \sf{v \: = \: 3(t^2) \: - \: 2(t)} \\ \\ \longrightarrow \sf{v \: = \: 3t^2 \: - \: 2t \: \: \: \: \: ...(1)}$

Differentiate (1) wrt. t

$\longrightarrow \sf{\dfrac{dv}{dt} \: = \: \dfrac{d(2t^2 \: - \: 2t)}{dt}} \\ \\ \longrightarrow \sf{a \: = \: 2(3t) \: - \: 2} \\ \\ \longrightarrow \sf{a \: = \: (6t \: - \: 2) \: ms^{-2}}$

____________________

Put t = 2s

$\longrightarrow \sf{a \: = \: 6(2) \: - \: 2} \\ \\ \longrightarrow \sf{a \: = \: 12 \: - \: 2} \\ \\ \longrightarrow \sf{a \: = \: 10 \: ms^{-2}}$