The acceleration-time graph for a particle moving along x-axis is shown in figure. If the initial velocity of particle is -5 m / s, the velocity at t=8 s is.

Question

The acceleration-time graph for a particle moving along x-axis is shown in figure. If the initial velocity of particle is -5 m / s, the velocity at t=8 s is. (A) +15 m / s (B) +20 m / s (C) -15 m / s (D) -20 m / s

Tardigrade Admin · Accepted Answer

The area under a-t graph gives change in velocity.
Given,

u = - 5 m / s

\Rightarrow

Area on positive side

= \frac{1}{2} \times 6 \times 10 = 30 m s^{- 1}

\Rightarrow

Area on negative side

= \frac{1}{2} \times 2 \times 10 = 10 m s^{- 1}

Net area

= 30 - 10 = 20 m s^{- 1}

Δ v =

Area

v - (- 5) = 20

\Rightarrow v = 15 m s^{- 1}

Q. The acceleration-time graph for a particle moving along x-axis is shown in figure. If the initial velocity of particle is −5m/s, the velocity at t=8s is.

+15 m / s

+20 m / s

-15 m / s

-20 m / s

The area under a-t graph gives change in velocity. Given, u=−5m/s ⇒ Area on positive side =21​×6×10=30ms−1 ⇒ Area on negative side =21​×2×10=10ms−1 Net area =30−10=20ms−1 Δv= Area v−(−5)=20 ⇒v=15ms−1

Q. The acceleration-time graph for a particle moving along $x$ -axis is shown in figure. If the initial velocity of particle is $- 5 m / s$ , the velocity at $t = 8 s$ is.