Question

Acceleration of a particle is given by an equation, $a = 2 + 2t + 3t^2$ when $t$ is the time taken. If the particle starts at $t = 0$ with velocity $2 \,ms^{-1}$, then the velocity in $m s^{-1}$ at the end of $2 s$ is

• A. 12
• B. 18
• C. 27
• D. 36

Answer 1

Answer: (B)

18

Answer 2

Here a = 2 + 2t + $3t^2$ i.e. $\frac{d \upsilon}{dt} = 2 + 2t + 3t^2$ i.e. $\int\limits^{\upsilon}_{u} \, d \upsilon = \int\limits^t_0 \, (2 + 2t+ 3t^2) dt$ $\upsilon - u = \int\limits \, (2 + 2t + 3t^2 )dt = 2t +\frac{2t^2}{2} + \frac{3t^3}{3} = 2t + t^2 + t^3$ = $\upsilon =2t + t^2 + t^3 + u = 2 \times 2 + 2^2 + 2^3+2 = 18 \, m \, s^{-1}$